Should I have clients buy their own hosting, or should I do it for them with a service that will allow me to have many domains? If I should do it myself what services are best?

You may do the following - charge your clients additionally for hosting their site, and buy the hosting for every client separately. It is better to tell them that you can host their site at this, this or this company. OR - you can by cheap but reliable hosting with unlimited domains allowed, (godaddy NOT RECOMMENDED), and host the sites by default and charge money for that - little bit more then you would spend for it...