To answer your question: After keyless, 6-keyed flutes are most common. 8 keys are quite common, especially in 19th Century flutes. One-keyed flutes are typical for baroque players, who are fully chromatic through the use of cross-fingerings.
4-keys: If you are used to a cross-fingered C-nat, you can be comfortably chromatic with 4-keys: Eb, F-nat, G# and Bb. Some flutes are made with that configuration. I’ve seen other key choices which I wouldn’t find useful for myself.
I hear people preferring short-F, but I’m more likely to use long-F, which works fine in the keys of C and F. Up to this point, I’ve only “needed” short F when going from Ab to F-nat, which showed up for me in C-minor (Eb).
The C foot becomes useful for tunes in C-major/D-dorian and F-major/G-dorian. I really love the key of F (with the related, D-minor & G-dorian).
Of course, in ITM, D & G (and related modes) are by far the most common keys. Next is A (fiddlers and old-timey musicians seem to have a lot of A-tunes), and then F & C.
If you think in terms of likely key signatures, I guess you might consider getting a 2-keyed flute with F-nat and G#.
But, the more common situation is that you require an accidental. G# and Bb can be achieved with cross-fingerings. F-nat is not so easy, and Eb quite difficult.
So, if I HAD to choose a 2-key flute, it would be Long-F and Eb.
I COULD live with a 4-key flute.
You can see why people skip straight to 6-keys or 8-keys.