Oh, this is something I'd like to see again! However, unlike in Emerald where you had to wait until the little Poke Ball next to their Match Call showed up; or in HGSS where you first had to find them outside their gyms, get their numbers, and could only call on certain days to schedule battles; or in BW2 where you could only battle most of them via the PWT and didn't get any EXP. or money (unless you count getting BP for beating three of them), I'd like maybe something like Platinum had, where you had different gym leaders you could battle each day, no calls or anything necessary. I was thinking of being able to battle them once a day, but Idk, that seems a bit too much, and, somewhat realistically speaking, it's not like they have that kind of time on their hands XD
As for teams, a full team of six with Fully Evolved Pokemon would be great! And maybe to spice things up a little, they could have decent hold items (i.e. not just Sitrus Berries) and maybe somewhat competitive-based movesets and Abilities and the like. As for money, I'd say roughly double what you got from the last gym leader (quadrupled if you sent out a Pokemon holding an Amulet Coin/Luck Incense during battle).