No worries about buying a cheap car that is what I have just done when my 1.3 diesel was scrapped due the ECU but that's another story.
All my car's have been second hand and I have always had to fix certain things myself my latest 1.2 Corsa came with a juddery clutch which I already knew was a common Corsa fault when the clutch is cold my old one used to do it, a fan that has a mind of its own sometimes I have to give the glove box lid a bit of a smack to get it working then it's fine and various bits of loose trim needed sorting.
I don't know what the situation is with the RAC but I would get a cheap multi meter mine was £15 but you can get cheaper then search the forum for checking a car battery voltage with a multimeter or YouTube there are loads of guides and the meter will tell you if the battery is flat and if the alternator is working fine, if you are lucky it's just the battery if unlucky it's the alternator and if you are very unlucky both.