You could host it yourself if you have a decent machine. You'd probably need to upgrade your internet package at home, at least to a business account and get a static IP. Also you need to check the TOS from your provider and see if you are allowed to run a server on a business account, this should be allowed for business. Also check to see if they have any data caps in place that may limit your traffic.
If I was you, i'd pick up a couple inexpensive rack servers on eBay and have one run PFsense as your firewall and just open up the outside world to the other server. You can run an Ubuntu server (or your favorite Linux distribution) and have it run Apache. This way you can have total control of your server, you can install whatever you want and host it with no ads.
How much traffic do you expect?