We use http://deploybot.com/ to deploy from bitbucket github and execute some commands like Db update etc.... works great, super simple and for free. You can dploy same repo on multiple servers too...

Interesting! Will definitely check the out!

You can try http://grandappstudio.com/roll-out/ for php deployment. The beauty is every thing that you wanted is well thought through. Have a look! You will love it.

You can also try https://www.amezmo.com (I'm the founder) for your PHP hosting and deployment!