I don't think there's any good criteria of eligibility really.
When I got bought for the first time I had nothing but some ladder ranking and CCs to my name, still don't have much and yet I'll be picked and play every season. I have faced the wide majority of elite players this game has to offer in my tier and went neutral or positive through each of the 3 seasons I have participated in (4th ongoing, we'll see).
If you want only the best to enter, just make sure managers are "forced" to tryhard in some way, for instance involving their own money.
If every manager has to pay say 20m to signup (if picked), and then you share the "manager prize pool" between managers from 1st to last at the end of regular season, they will be forced to try in the auction, and try every week until the very end.