Here is the sort of thing you can do if you know how to read treble recorder notation at pitch. Look at this one:

Fly Me To The Moon

That is in fact, sort of, playable on a C recorder. But it sits very low in the range and can't be very effective on it; there is also one rather icky fingering movement, the chromatic run up from low C. Play it on an F recorder and it sits right in the most effective part of the instrument's range - it will sound very much better and it's easier to play.

There is an even larger difference in playability with this one:

Softly as in a Morning Sunrise

Apart from the issue of acoustically effective range, you have to get round those low E flats. On a C recorder they're half-holed, which makes them hard to play accurately at the speed required (even though this isn't a particularly fast tune). On an F alto those passages fall under the fingers a lot better.

A rather small effort in learning to negotiate the notation means you can save yourself a lot of struggle later on with the actual playing, and you can just pick up a larger variety of scores and just play them. (Everything I've looked at on that French jazz tunes site works fine on an alto F recorder, even though the compilers can't have had it in mind).