We need a little more info. Are you planning to do the site yourself? If so, how much programming and graphic arts experience do you have?
Let's assume you're going to do the site yourself and you have some coding experience, but not a lot. I personally would go with Zen Cart. It is highly customizable, it's free, there's a huge support community, there's a module for almost anything you can think of, etc. If your server is using cPanel, you most certainly have access to an installer like Simple Scripts which can install Zen Cart automatically for you.
Unless you're planning to do a mobile site in addition to your actual site, I would stay away from flash since iphones and ipads can't use it. There are millions of people who do the majority of their surfing from those devices.
To accept credit cards, you need to setup a merchant account and a payment gateway from your bank account to your site. You can also use paypal. There are modules for setting both of these options built in to Zen Cart. I don't think you'll have much luck getting out of paying transaction fees.
Hope that helps a little