It depends on what coaster you ride. Most of the steel coasters have over the shoulder restraints (OTSR), and a good majority of those have an additional seatbelt that connects the OSTR to the seat between your legs. Wooden coasters usually have a lap bar and seat belt combination.
As long as you are properly seated, and your restraint is secure, and you don't try to stand up, you'll be fine. 99.9999999% of ride injuries are caused by the rider doing something STUPID, rather than the ride malfunctioning.
Just out of curiosity, what park are you going to and what coaster will be your first?
Oh yeah, one more thing ... DON'T FORGET TO BREATHE!! Passing out from lack of oxygen as you're going down the first hill is no fun at all.
And have fun!!