I started out with POWER shoes. Not sure if these even still exist, but when I had them, they were the "Nfinity" of the early 2000s. Nobody cared about having the lightest shoe, or one that claims to help you tumble better..they wanted the blue rubber. And if you don't know what the blue rubber is...
I got Kaepas after 2 seasons in POWER. Hated them. Heavy and had weird laces.
Then Nfinity came out. I had the Genesis, Genesis 2.o, Evolution, Tyger, and Vengeance. And in multiples. I'm loyal to my favorite shoe company because I always had great results.
Somewhere in with my Nfinities, I had to get Nike Cheer Flash for HS Cheer, and they were awful, and actually progressed my ankle injury that we have been putting surgery off on till I'm done with college. They were like wearing bricks. My Physical Therapist then suggested I wear High Top Reeboks for school cheer, and I actually loved them. I could still wear my ankle braces but I had the extra ankle support I really needed. The soles are also quite a bit thicker. But they are very lightweight.
There's my input lol. :p
ETA: My first year at CSA we were required to wear the No Limits. Wasn't very fond of them however I have heard their new shoes have much better reviews. I ended up replacing them and switching back to nfinities and then was required to buy Varsity Last Pass my third year. Also did not like this shoe. It was very stiff in a bad way...not by good padding, but by an awkward, not comfortable sole.