grrr.. I just had a long response written out for you, but I hit the back button on my mouse as I went to post!!
Anyways, I would talk to your recruiter and see what he thinks of your waivers. I myself told him that I had smoked pot a couple times in my past, but we kept that on the down low

. (It was very awkward because my dad was next to me when I said it...I shoulda kept quiet!!!!).
If your recruiter thinks you have a good chance of getting the waivers signed (which you probably do) then go to MEPS. Make a lovely night out of hotel food, ASVAB, physical, medical, NFQT if you need it, getting your butthole examined...oops sorry I ruined it for ya.
After you get all of the examinations and tests finished you will wait in a waiting room for a counselor to call you up. This can take a while. If you qualify then they will guarantee you Navy Nuke right there if you want it. If you don't qualify and need some waivers then your night will be delayed quite a bit. You may even have to go home and come back. I was lucky enough to not have to fill out any waivers, but the guy next to me was on his third visit to MEPS.
edit: you also go over your bonuses here. I got $8,000, but that depends on when you sign up (theres a post here somewhere discussing that).
You don't have to make any binding contracts at this point. You will not be obligated to force the Navy at ANY point in time on your first visit to MEPS. Even if you raise your right hand you will not be obligated to ship until you raise your right hand again on your second visit to MEPS right before you ship (correct me if I'm wrong). So it doesn't hurt to go down to MEPS and see what happens. Its good to get all of that crap out of the way ahead of time anyways.