As a newly enlisted E1, which bank is good for my direct deposit and for using down the road for car loans?

Don't get a car. I am amazed at how many folks I see simply driving their car from barracks or work site to the DFAC that is a 10 minute walk away. Consider instead, putting 30-50% of your paycheck into savings at one of the mentioned credit unions. Assuming you are single and living on post, what do you need the money for anyway. Partying and food will burn a hole in your pocket. Sure, there are times when you will want a car to do stuff off base, but with military rates at most major rental agencies, you will spend way less on car rental expenses then you would spend on monthly car payments and fairly expensive insurance. (You are in a demographic that tends to be more expensive to insure).

If you can learn to live on this budget for a couple years, you will be surprised what you end up with in the bank. You may even have enough to almost pay off a decent used car up front. You should also consider trying to build up good credit. You are also in the demographic that a lot of credit card providers like to offer cards to, knowing that the typical one will likely max the card rapidly and pay minimums. My suggestion is to set up that savings account as I mentioned earlier, and get a credit card. Set up some sort of automatic payment to your card that pays it off every month. Again, after a couple years of this you will have established decent credit and have a good base savings.

NFCU or USAA all the way. There are no better choices.

USAA, PFCU, Navy Fed Credit