You don't have to use the same host but if you are going to be the go-to-guy for all their needs then it would be a good idea to have them use the same web host provider allowing you to be familiar and proficient with one control panel format because not all hosting companies lay out the panel that same way and some may have more or less features.
Ideally, you can get rent one of their dedicated servers where you can manage all the hosting for each of your clients. That way you reap the benefits of having all your clients' sites under one roof plus you keep a little profit for yourself. However, to make it worth your while you will probably need 6-12 hosted sites depending what you would charge for hosting. Typcially, depending on the size of each site you host, you could host about 30-60 clients.