Hi! It does let you sign up for a date and time you want. However, the times listed are in Central Time Zone, so have that in mind when you sign up. When I signed up for my test, I signed up too late so only the 5:30AM slot was left for the date I took off work so I had to take it. I would sign up ASAP so make an account now, and check periodically for the January dates to come out.
I would start preparing for the TEAS about 6 weeks beforehand (general recommendation). The test is very doable, with proper studying, you'll do just great! I recommend getting package of your choice (Practice Tests, Study Manual, Online Modules) from the ATI website. They give you only the information you need to know, which simplifies the test greatly. Hope this helps, let me know if you have any other questions!! 🙂