Nachum, I’ll try to hit all of your questions.
Keeping kosher: This should be technically possible. However, it will require a good deal of prep work on your part. Before heading to boot camp, I would contact the Jewish chaplain on base (or the nearest one available) and let him or her know about your situation. They may be able to provide you with kosher MREs for the duration of training. That’s the only 100% way to keep kosher. I know guys that just ate vegetarian at the mess hall, but that may not be acceptable to you. Realize that you will probably take some flak for having special meals for you. It’s not because your Jewish, but rather that you are doing something “out of the ordinary”, which is not liked by any drill instructor. But hey, if it’s important to you, deal with it for the short time you’re there and then you can spend the rest of your time in the Army making your own food choices.
Davening: 3 times a day might be difficult, but you can (usually) get up before reveille for morning prayers, and you can usually find time before or after lights-out for an evening session. Both of these will be in the dark, but it’s better than nothing. Also, you should work on your speed-davening. I wouldn’t count on more than a 10 minute period each time.
Kippah & Tzitzit: You can probably wear a kippah under your cover, but that might be something you want to talk to the Jewish chaplain about ahead of time. There are some activities that it just would not be practical for though. Realize that you will have a completely shaven head and I’ve never seen a kippah that could stay on during the kind of movement you are sure to experience at boot camp. Tzitzit is do-able if you can keep it out of sight. I know you have some concerns of where it will touch when tucked in, but I’m sure you can get creative on ways to keep your fringes in line.
Tefillin: I’m sure it’s allowed, but you may not have the time to wrap whenever you like. Again, refer to the davening answer. You will have the opportunity to attend Jewish services on most Sundays. It ain’t the ideal scenario, but it will allow for much more devotion to prayer and such.
The advice I give most people is that you will have to compromise on some things. That’s a part of military life, no matter what your religion is. If you are unwilling to compromise for 6 weeks, then the military is not for you (which is OK). Once you make it through basic training, it gets progressively better until you are eventually in the regular forces and then you can make a lot of these decisions for yourself. With a few occasional exceptions, you should be able to observe most of the mitzvot. It often takes some advance planning and some additional effort on your part, but it can be done.
Which service: I don’t know of any service being more tolerant of Yids, but you may want to consider the length of boot camp and initial training. That’s the toughest part (observance-wise), so if you can keep that short, it should make things easier. Also, you might want to consider picking an MOS (job) that keeps more regular hours. Everyone deploys, but there are always jobs that will require more weekend duty, etc. You might also consider becoming a chaplain assistant. It’s not as big of a process as becoming a chaplain, but you still have first-hand access to religious resources.
I hope some other people will chime in here with some other experiences. In the meantime, here are a few examples of people who were successful in this endeavor:
Joe Kashnow
Mike Ekshtut