Low Limit Credit Card
I keep a 'special' low limit credit card, which is only good for US$2000, specifically for internet and other 'risky' purchases. It's from my local credit union and they call me just about every time I use it to 'verify' that I purchased what ever it was. It's the only credit card 'company' that ever calls me like that that I have found.
As to credit cards on the internet, I haven't run into any problems over the years, but I'm relatively careful. And I never follow an email link. I look at the email 'source' code and often the actual link is to a forwarding site.
I do like to have some fun now and again, though, so sometimes I click on the link in the email and put in my credit card number (with a few 'changes'), a fake name and all that and 'submit' it just to get some garbage in their database... This is common with PayPal phishing schemes. It really does look like the real site. But, it's obvious from the URL (and usually other 'small' details) it's a phony.
Last fall I did get two scam charges. I don't know where they got the info, but they had my credit card number, name and address and all that, but they had the wrong PIN code from the back of the card. One was charged and then there was a charge back the following day. The other one (American Singles) charged me and didn't do a charge back. I found this when I got my bill. My credit card company (I called them right away) credited me for the amount right away and issued a 'dispute' with American Singles (Both bogus charges were at 'Dating' sites, but I've never been to a dating site). That was the last I heard. The next bill showed the disputed charge credited back to me the same day I called them (and I could see it online as well, for that matter).
So far I've been lucky, but my advice is simple: Make sure the credit card company (or companies) you deal with have a US$50 fraud limit, and that they will do an immediate charge back and will send the company doing the charge a 'dispute' notice. I use Emery Federal Credit Union for my low $ card. Their calls to me to verify charges do take a couple minutes, but it's a good feeling that they're watching charges closely.