No problem! GMing is tough, but your initial sell was just fine! I just had the follow ups which you answered for me!

I think just using the name "Valkyrie League" for the in-character group/league is perfect because it already evokes the kind of feeling you seem to be going for (the organization looking for the pinnacle of "warriors"). As for what direction you go, whatever you think will be the most fun is probably best so interest stays. Training league with a group of friendly rivals that grow and compete against each other definitely has a more "sports anime" feeling in my opinion, and everybody loves seeing character growth, but there is merit in starting with high level characters too.

Or maybe split the difference and have the recruiters be those dudes in the gyms giving advice to people challenging them, and participants get scouted for Valkyrie training program after X number of badges? To weed out the weak early without spending real time or resources on it lol. Then you can still have recording, practice arenas, and transport going on to test out their chosen trainers against various regional leagues. Really I think either way works so just go with what seems best to you!