Hi linder, welcome to SitePoint!
There are really two main routes you can take: a fully self-hosted ecommerce system (like [magento) or a 3rd party hosted service (such as [URL="http://www.shopify.com/"]Shopify](http://www.magentocommerce.com/))
The first option is great in that you can get the whole system for free and set it up to your heart's content. The downside is that they are very complex, and all the issues of security etc are on your shoulders (you need to set up SSL certificates etc). In my view, unless you specialize in this stuff, it's too hazardous to get into... but you may be smarter than me!
The hosted solutions are good in that all the security is done for you, and the whole system is alreay up and running. You can seamlessly integrate it with your site, including CSS, and even the url can be made to look like a part of your own domain name (well, at least with the better services). Your client just pays a monthly fee for the service.
That's my take on it all, anyway.