I think you'll be happy, Janet.
What I do is have one credit card that I only use for online purchases. If anything goes wonky there (and it hasn't yet after many years of this use), it'd be easy to cancel the one card and get a replacement.
I did have one instance of credit card fraud that I had to deal with but it wasn't with my "internet card". I think if you stick with secure sites and reputable dealers you'll be fine.
