Verisign does a wonderful job of protecting your information. The next time you go to a website the Verisign logo should be clickable. (or at least it used to be. I haven't checked in a while) It should give you information about that particular site's registration and security as viewed by verisign. You can usually trust those sites.
For example, I just looked at
Aquarium Supplies, Pet Supplies and Pond Supplies by That Fish Place - That Pet Place. You'll see the verisign logo, as well as a McAfee and BizRate logo at the bottom of the page. While I can't vouch for their products, they are verified secure.
Another option many sites allow for is paypal. This is a highly trusted site you can link to your bank account and, in some cases, use just like a credit card. If I were to buy anything off a site like ebay or aquabid I would use paypal.
Does that help your sense of internet security?