Regarding pay: $2828 is the BASE PAY. Depending on the area you live in, you will receive BASIC ALLOWANCE FOR HOUSING (BAH). This is to offset cost of housing depending on where you live. You will also receive a BASIC ALLOWANCE FOR SUBSIStENCE (BAS); this is fixed at $223.04 per month. If you are at a sea going command, you are entitled to SEA PAY. If you are a submariner, you receive SUB PAY.
I encourage you to talk to your recruiter about pay and entitlements when joining the military, and then fact check him on your own, as it seems you're doing.
As far as being a "soldier": you're joining the Navy, most likely you'll be a SWO(N) or a Submariner, so you are first and foremost a SWO or a Sub guy. You'll go to nuke school, do your time on the ship, get your pin, and meet all the other wickets for a Navy Nuke.
Afterwards, if you stay in, there is a chance that you could support GWOT, either voluntarily or involuntarily. Chances of this happening depend on a number of things, and are really unpredictable. If this (probably slim) chance is a deal breaker for you, then consider that the military might not be for you. I know plenty of submarine officers and a few SWOs that have NOT had to go directly support the GWOT overseas, and only a handful that have. Most of those were by choice, some were not. If you use that as a probability of having to be a "soldier", then the chances are unlikely.