Geppetto....
this one's kinda hard to answer; it all depends on how far you want to go..
The most common would be hand saws, tenon saws and dovetail saws, each available in rip and cross cut as well as a variety of lengths. In addition, there's fret saws, bow saws, coping saws, veneer saws, gents saws, flush-cut saws and a whole multitude of others... the trick is to figure out which ones you need to suit your style of working.
It's a bit like hand planes... you either don't use em at all, use a certain few or you need dozens of em.... there's no set "right" answer.
Like hand planes, I've learned that quality costs... buy the best you can afford and they shouldn't let you down... that said, quality needn't cost a fortune...