Olivier - don't worry about it too much! I think it's fair to say that if it's got teeth, it'll cut wood - and all the better if they're sharp. Vintage or modern, resharpenable or hardpoint, doesn't really matter - they all cut wood. Whether they're rip or crosscut matters rather less than their being sharp, in truth!
There does tend to be a lot of discussion of relative minutiae on internet forums. You'll find people arguing about whether rip saws for softwood should have 5 degrees of rake or 10 degrees of rake (both will cut perfectly adequately, one may be marginally faster than the other). You'll find deep discussions about handle hang angles, whether canted backs help prevent overcuts at the back of a board, how many thous of set they have on their saws, and all sorts of other stuff - usually from people who don't do much sawing.
In general, use big saws with large teeth for deep cuts in thick stock, and small saws for shallower cuts in thinner stock. If you can find a saw with a comfortable handle, that's a nice bonus. Sharp saws cut much better than dull ones. Rip filed saws cut better along the grain than crosscut saws, and crosscut saws cut a bit better (but not dramatically better) across grain. Once you get tooth sizes smaller than about 12 tpi, it really doesn't seem to make much difference whether saws are filed rip or cross, but it does make a difference with bigger tooth sizes. Sharpening rip-toothed saws is easier than sharpening crosscut toothed ones, especially when they have small teeth, like dovetail saws do.
And that, pretty much, is all anybody needs to know about woodworking saws. Most of the rest is opinion or personal preference.