Whew, that's good to hear. Gelcoat repairs are pretty straight forward, and are as good an initial DIY project as any other.
Hope you don't take this the wrong way, but you seem pretty new to all this. Any chance you can get somebody with boat ownership experience to go with you on your trip this weekend? There are tons of things that merit close inspection when evaluating a boat, and if you miss them you could easily wind up getting a boat with a negative value (i.e., it'll cost more to make her seaworthy than the boat is actually worth.) That's not to try and scare you off, but just trying to make sure you go into this with both eyes open, so to speak.
If they truly are spider cracks that go no deeper than the gelcoat they are likely due to age and post cure shrinkage ( no ! not like of Seinfeld) and not worth fixing. To properly repair widespread but cosmetic hairline fractures will cost more than the boat is worth. If you repair them improperly ..... they'll be back next year.
Paint the bottom and go sailing.