With the lack of players willing to put a lot of gold/money into pvp gear atm a budget league would certainly be interesting.
When I think back to D2 budget leagues often had a list of legendaries that are allowed. Something like that could work in D3, supply of low-mid items is high and they are dirt cheap. List could look something like
"Mempo only without Crit and Mainstat/Vit affixes", "Echoing Fury only with one of socket or crit damage or mainstat/vit affixes" and so on.
Should be paragon0 for that too, the disadvantage of low paragon (which has nothing to do with pvp) would become too big if all use similar gear. A lvl60 char takes like an hour now and it allows players to play more than their main char.