Off the street, you're probably going to be doing a lot of hanging out and doing nothing of substance while you wait for training. They'll put you in some AFSC for purposes of enlisting, but it may be completely unrelated, and not even in your hiring squadron. Just depends. Even then you'll likely still do nothing. Thats been my experience at least. I just use drill weekends as a time to continue to get to know the pilots. There are a lot of briefings you won't be able to sit in on at this stage without a TS clearance. I've never heard of units giving new-hires rides. Those are typically reserved for dudes who have done something special or have shown exemplary work ethic in the squadron. But, I also dont know jack, so YMMV. Also, its entirely possible to do you FC1 before you enlist with the unit, there were several guys at my FC1 who had not enlisted yet. But its beneficial to enlist asap, because then you get paid during drill. I think if you live a ways away from the base its a different story. If you've ever had any surgeries (aside from simple things like wisdom teeth) start getting all of your med records from that surgery. It can take a while for Dr. offices to get those, and you'll need them for MEPS.
What you could do, and I've started doing so as advice from one of my units pilots, is start tracking everything you have done/will do post-hiring. Make it into a neat document for future hires. Things like what you had to do getting uniforms ordered, or computer access, anything that will be useful to the next guy getting hired. If there was some little trick you found to get X done quicker. You'll soon find out everyone on base acts like you're the first guy to get hired off the street and no one knows what the heck is going on. Even though that's not usually the case.