...how do i do this over a website? All of the hosting companies that I have seen (splash, site5, aletia) don't seem to offer plans that include help with taking credit card orders. So where do I go if I need to do this?

You need a merchant account. A few years ago hosts were offering this as included. That all changed as setup fees and stuff have been added. It would be nce to still offer this but the fact remains that gateways require at the minimum a 99$ setup. Back then it was nice to offer a ecommerce package and not take losses. It was like offering a company out of the box so to speak.

I don't mind setup fees, I think it is a nontrivial thing for a hosting company to go and I don't mind paying for it. What are some good hosting companies that do this?

www.www-hosting.net is one that offers merchant accounts with your hosting.