Nursemike? gave you some good information here.
I'm a Registered Nurse in an Intensive Care Nursery (often called a NICU, pronounced "Nick-You"; NICU stands for "Neonatal Intensive Care Unit".
First I'll give you some background on neonates, then talk about nursing schools, and then give some little pointers to hopefully help you out as you make your way into the neonatal nursing arena. This is a long post so be prepared to read for a few minutes... I tend to type fast and talk a lot!!!
To get really specific, a neonate is a baby who is up to 28 days old, then they are called infants until they are a year old. After that they are toddlers, school age, adolescents, etc.. All children are grouped into the heading of pediatric patients, which basically means children. Neonates are very special children because they are transitioning from being inside their Mom to getting along in the world on their own. A neonate can be a full term baby or a tiny premature one... simply a baby 28 days old or less.
Nurses take care of children in many hospitals, clinics and doctor's offices. In larger hospitals there may be a special "Pediatric" unit where children come to be hospitalized. This usually includes children up to around 16 years old. A baby who is just born and goes home but must return to the hospital for some reason would go to the pediatric unit too, even if he is less than 28 days old (a neonate). The reason for this is because the Neonatal Intensive Care Nursery and the Well Baby Nursery (which is part of the hospital where mother's give birth) are intended to be kept as free of germs as possible. A baby who has left the hospital could pick up germs that we would not want in the NICU or Well Baby Nursery. There are also Intensive Care Units for incredibly sick children which are often called a PICU meaning Pediatric Intensive Care Unit where a neonate who is too sick to be admitted to the regular Pediatric Unit would be kept.
Anyway, to be a nurse you must decide if you want to be a RN (Registered Nurse) or a LPN (Licensed Practical Nurse) because they go to different nursing programs.
LPNs are usually taught at 2 year community colleges or Technical Schools. The program usually lasts one year. When you graduate you will be qualified to take the state licensing exam called the NCLEX-PN. If you pass that exam you will then be legally allowed to call yourself a LPN/Practical Nurse/Nurse.
RNs are divided into other categories according to how long they go to college. There are some community colleges who offer an Associate Degree in Nursing (called an ADN) which is sometimes called Associate of Science in Nursing (called an ASN). I think ADN is the more common terminology. An Associate Degree takes two years to complete. When finishing completing the 2 years of nursing school you are then qualified to take a licensing test called the NCLEX-RN. You can not work as a RN without having passed this test (which used to be called "State Board Exam"). After passing the NCLEX-RN you will then be allowed to write "RN" behind your name and call yourself a Registered Nurse/Nurse. Another way to be able to take the NCLEX-RN exam is to go to a 4 year university and take nursing school classes to obtain a Bachelor's Degree in Nursing (called a BSN). The first two years are spent taking more liberal arts type classes and the second two years are more similar to doing the Associate Degree 2 years knowledge. At the end of the 4 years you will receive a Bachelor of Science in Nursing degree and will be qualified to take the NCLEX-RN exam and if passing that test you will be able to put RN or BSN behind your name and call yourself a Registered Nurse. The BSN programs often have more content for things like community health nursing, detailed assessment courses, nursing research, and management classes. The ADN graduates and the BSN graduates each take the exact same NCLEX-RN exam to be licensed as RNs.
A BSN degree is often required to be a nurse manager and is required if you want to continue on and obtain a Masters Degree in Nursing (MSN). Depending on which, Master's program you go to (there are specific ones at different universities) would help you to qualify to work as a Nurse Practitioner, Clinical Nurse Specialist, Nurse Anesthesitist, Nurse Educator, Associate Nursing Professor, high levels of Nursing Management, a Midwife, Nurse Researcher and several other options I'm sure I've forgotten to mention.
You can continue on after having the Masters Degree (called a MSN for Master of Science in Nursing) and obtain a Doctorate in Nursing where you can put Ph.D. behind your name and people will call you "Dr. Jane Doe". Usually Nursing Researchers and Nursing School Deans and Professors have their Doctorate Degrees. I remember thinking how cool it was when I found out that there are nurses who are addressed as doctors. We had several professors at my university who had their Doctorate Degrees and our Dean of the Nursing School had her doctorate. By the way, Ph.D. means Doctor of Philosophy.
So you see, there are many paths to becoming a nurse and many levels of nursing education. Some BSN programs have a BSN-to-MSN program where you go straight from beginning student and graduate with a Masters Degree before ever taking your NCLEX-RN exam. It seems like more and more people are going straight to the BSN programs if they have the time to spend 4 years in school. Usually young people, like you, do the 4 year program because you are young and have more time and get to really enjoy the university experience. If you decide on the 2 year Associate Degree you can begin working after 2 years of school and then if you decide you want to get your BSN, then you can usually find a BSN program at a university (or even online sometimes) to take classes part time. In the end you have a BSN and it takes about 2 years to get the BSN part (since you already have the 2 years spent doing the Associate Degree education). That's what I did because I was 28 when I went to nursing school and didn't have the 4 years to spend... had bills to pay and stuff like that.
I suggest you talk with your high school guidence counsellor about your desire to be a neonatal nurse. This person should be able to help you find all kinds of programs in your area, find out what you need to be able to apply to the college, and make suggestions of things you can do while in school now to help you be successful entering and finishing nursing school. Once you graduate from whichever nursing program you choose you will take either your NCLEX-PN (to become a LPN) or your NCLEX-RN (to become an RN) and then you can apply to work in a place that takes care of neonates like a NICU, Well Baby Nursery, Labor & Delivery Unit, Mother Baby Unit, Pediatrics, PICU, Pediatrician Doctor's Office, Health Clinic, or many other places I'm too tired to think of right now.
I'd also suggest you call the hospitals in your area to find out what degree the nurses need to have to work with neonates. More and more NICUs are requiring only RNs to work in their units so if you become an LPN you might not be hired there. Each hospital is different. All the NICUs I've worked in require RN degrees. Some Well Baby Nurseries, Pediatric Units, and Doctor's Offices have LPNs working there.
Many nursing students enjoy working as unit secretaries in hospitals and this is great experience. Some hospitals hire nursing students to work part time while they are in school to positions similar to Nursing Assistants depending on how far along you are in your nursing program. These things look very good to potential employers and could help you get the neonatal position you want. I remember working in a hospital during my last year of nursing school. I did no work with neonates or children of any kind though. They offered me a job on a floor for patients with heart problems. I enjoyed it very much and learned a lot. Anyway, when my college graduation time came we all began to apply for positions as Graduate RNs and those of us who had been working in the hospital as students were given first choice of which department we wanted to work in. I chose the Well Baby Nursery and absolutely loved it! I'm so very glad they had a position open for me!!! A year later I was working on a Mother-Baby unit and then 6 years after that I transferred to the NICU which is where I've been ever since.
Whatever you decide to do, be sure to study very well in your high school classes! Nursing school can be very competitive these days to get in to and you want to have good grades, especially in science and math classes. If you can do some volunteering at local hospitals (anywhere in the hospital... not just with neonates) during your summer breaks and such that would look good on your nursing school application.
Again I suggest you contact your High School Guidence Counsellor for help in this area. Learn to make use of your resources because Guidence Counsellors are very skilled at helping you find your way to the future you want to have.
To answer your actual question which was: "I don't know which type of nursing I should major in to do this." my short answer to you is this: A nursing program that gives you an Associate Degree in Nursing or a Bachelor Degree in Nursing would give you the best chance of working with neonates in an Intensive Care Nursery these days. Small community hospitals would give you more of a chance if you choose to be an LPN instead, but not always. Find out what type of nurses your local hospitals require; that should be a really good starting place for you as you make your decision.
By the way, when you graduate from either an Associate or Bachelor program, you are considered a "Nurse Generalist" meaning you know a little bit about all kinds of nursing.... enough to be safe to take care of patients but you are not an expert in any one area. (Sometimes in nursing school you will realize that you like a different field of nursing rather than the one you originally thought you'd like. If I could not have been accepted in a department that took care of babies, my second choice was in a psychiatric department. I would have never thought I'd like that area until after I wnt to school and found out how interesting and rewarding that area of nursing can be!) Anyway, after nursing school when you pass your NCLEX exam you will then choose the area of nursing you would like to specialize in and then apply for a job in that department of a hospital or clinic, etc. and you will then be paired with a seasoned nurse in that department who will be like your buddy (called a Preceptor) and show you how to do your work. There is still oodles to learn once schooling is finished and then usually in about 6 weeks to 3 months or so you will be on your own like all other working nurses. You will always have other nurses around you to help you and eventually you will be helping other new nurses learn who come to work after they graduate too. Another important thing about nursing and other medical fields is that the learning never ends... NEVER. Progress is made each day in knowledge of health conditions, new treatment options, new drugs, new technical equipment, yada yada yada. If you don't enjoy learning and don't like the thought of having to keep up with new things in the field, you might reconsider becoming a nurse. Just realize that this is a very important part of being a good nurse.
I apologize for talking so much about this and for this post being so very, very long!!! I also hope my information has been helpful and if I can answer any other questions for you please feel free to let me know.
Wishing you all the best, always!!!