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I would want it to be a hub for the series going forward where I could keep everything I trained that I wouldn't want on HOME. More importantly, I would want it to be a place where you could screw around with the rules, train Pokemon, and battle with preset rules (much like the previous entries) against preset 6v6 teams where I get a team preview. I never really cared for the minigames if I am being honest, but if they went towards getting points for training/item unlocks, I would be okay with them.
The most important aspect for me is that they would release it as digital only, have HOME integrated so that you can add/remove Pokemon from HOME without the HOME app launched, and so that it had all Pokemon available. It doesn't need a scenario mode like Colosseum; it should be more like PBR but also with a hub for training/leveling/potentially breeding Pokemon.