First, welcome to RF.
The above is good advice.
I don't think online purchasing is any worse than using a credit card in a store if you take good precautions. In any event, I've never had a problem (so far).
Here's my list which includes what others have written:
Use a good anti-Virus package. Personally I'm using Norton with LifeLock but there are others.
As noted, use one site such as PayPal that lives and dies by being secure. They have a strong interest in not having people use them to rip off others.
Use well-known sites. Without going into how you can check other sites that are not well known, I'd use major shopping sites that are associated with stores or Amazon.
If what you're looking for is only available in a small online location, try to use a on-time credit card as noted above. Don't use a debit card.
If a site starts asking for more than you need to make a purchase, name, address, payment type, I'd back out.
Set your browser, depending on which you use, to a "private", "InPrivate" or "incognito" window before shopping. It's not perfect but a real help.