When I was recruiting my DEPs got BAH if married, or had a dependents, while in basic and AIT as well as being enrolled in DEERS.
All the benefits start once you start Basic, there is no waiting period.
If you got married after you enlisted but before you ship to Basic make sure you take your Marriage cert to your Recruiter. I would also go back the court house or, wherever they have it, and get two other "originals" from them, one for MEPS and one for Basic. You shouldn't have to have one for each place, you Recruiter should take care of it at MEPS, but in case he doesn't it is best to be prepared.
01 TJ, 34 Super Swaper 34x10.5 bias, Winch, locked, belly up, some armor.