I can understand your apprehension, but a few things to make you feel better.
1 - If your PP info was stolen, it was most likely because someone was tracking your computer, you stayed logged in somewhere, of you had a malware program on your computer that you weren't aware of. Or Your PP password was the same as some other password. Etc Etc, there are a number of things it could be other than PP
Honestly, I've been using PP exclusively to take payments for the business I run (for 7 years), I've never had any of our information compromised, nor have any of my clients.
2 - Paypal asks for the information because it is considered a Bank Account according to US institutions. They need to to verify your identity. Their webpages are secure insomuch that your computer is secure.
3 - Credit Cards are THE MOST SECURE form of payment available other than Paypal (debit cards are the LEAST SECURE). Our company used to accept credit cards, however the security protocols that are required are pretty ex-tenuous (and pricey, so we stopped and only accept PP.) Because of that, CC companies offer full refunds for any manner of fraud. So I wouldn't worry about any of that. I buy pretty much everything online with CC's.
Basically, if anything happens your covered with both PP and CC's. So I wouldn't worry about that.
Anyway, just thought I'd let you know.