Been shopping online for years with normal credit cards at all kinds of sites and I haven't had any issues. It's not like shopping in real life is risk-free either. Credit cards can be compromised in many ways at retail establishments, restaurants, whatever. Employ the same common sense that you would during any other transaction and you'll be fine.
Credit cards offer good protection against anything that goes wrong anyway. Just don't put yourself at more risk by shopping at really shady places.
Otherwise, don't put too much stock in any one given site in terms of prices. There are a lot of sites like Shopbot that can search many merchants and point you to the one that has the best price on a particular item. So shop diligently and compare merchants, keep in mind any taxes and shipping charges. not all sites are equal in that regard and it can make a big difference in the overall price.
I think that's about it?