You could use a MBaaS solution, which provide tons of features (including those three):
Braincloud you already mentioned.
or you can use specialised services for each feature you need. There are plenty of service providers for leaderboards, socket data or push notifications.
It totally depends on your needs. E.g. amount and features of leaderboards, socket features, amount of push notification per minute, free plans, paid plans with/without SLAs, guaranteed uptime, support and so on.