Each option has pluses and negatives.
The best suggestion would be Google. They're not exactly going anywhere, any time soon, so the server *should* still be there in future.
GooglePlay has its own ecosystem, but then OUYA players can't access it.
The best option, in my view, is to make your own. It's going to be complicated, and thwart with security dangers, but if it's yours, on your server, then theoretically any and all versions of your game(s) should be able to access it.
Also, because it's your server, any downtime will be your own issue, and not a case of "that company just broke my game.."
But it's a long road to get it all working.
... Good luck with whatever it is you choose.