Don't become enslaved to the stereotype that rock demands bright, focused cymbals, whereas jazz and fusion call for darker, more diffused tones. Some rock drummers like dark cymbals, just as some jazz drummers favor bright ones. Cultivating your own sound makes more sense than acquiring a plethora of equipment to be switched out depending upon the genre you're playing. More important, given that you're "pretty new to drumming," your attention should be centered on technique, not on gear. Zildjian As are highly versatile and should easily cover all your bases for the time being. You have all the equipment you need. Put it to use with disciplined practice.
Top advice, having one ride that can cover a lot of ground will save you a lot of money in the long run.
A's will handle any genre you throw at them. The only thing with B20 cymbals is they have their own individual nuances but that's an argument to be had for another day (and one that happens nearly every other day here!)
I personally find a 20" A Medium a bit too light but the 22" A Medium is a different beast altogether, bit bigger and heavier but gives it a bit more darkness and control which is what you're after.