How to start.

If you look at the top of the page there is a section of "Specialties". If you go to that there is a section under that labeled "Government/Military Nursing". People on that section would probably be able to give you specific advice.

You can do your prereqs while at your next duty station. I am a former corpsman, and I took classes two at a time while on active duty. You won't be able to do a nursing program unless you apply for the commissioning program (it's different now, and I can't remember the name of it), but you can be ready to go when you get out to use that GI Bill for nursing school. Then use it to get your BSN, because it's becoming more and more important to have a bachelor's over an associate's, and since it will be covered, you might as well.

You can take some general ed stuff online, but most of the prerequisites require at least some portion of the class to be taken in person (unless you want to take one of the VERY expensive online classes that mail you the lab stuff, which seems fishy to me, anyway).

You may be able to get a CNA job as a HM. I was offered a few positions as one, and I was able to get the CNA requirement to my BSN program waived as well.

Interesting they moved HM school for Fort SAM Houston! I remember it being in Great Lakes! :)

Skip the Associate. You've got the time and the money for your Bacchelors!

Good on you for wanting to get a jump on it! Once you get settled at your duty station, you go by education and training and they can help steer you. There is tuition assistance (though it gets cut off at times based on national budget issues) while you are in the military and make sure you use your GI bill. Get started on the prerequisites (maths, English, psych, chemistry, etc). Those all are necessary for an associates or a bachelors in nursing.