I don't do a lot of Internet buying--but IMHO using a US credit card (don't know about international laws) is the best for on-line transactions.
CC: Credit Card company is, by law, considered to be one of the selling parties and responsible for ensuring the transaction is satisfactorily completed. If you cannot achieve resolution with the merchant, going to the CC company will get your money back (even if temporarily) into your account until resolved. If you win, the CC company will have to get their money back from the Merchant. Also, you are liable, at most, to $50 of fraudulent CC use. Some CC companies offer 1 time use numbers if you have concerns about CC number leaks. Merchants seem to usually lose CC challenges by customers.
ATM Card/Debit Card: Looks like a credit card, and may be operated by a CC company. However, this is your checking account. You cannot stop a check written and given to a merchant if you have a complaint about the transaction--that is fraud on your part. There is no limitation of liability for fraud on your account--if it is drained, you loose the money until you can (if you are lucky) find the responsible party and get the money back from them (not the bank or CC company). Checks and checking accounts have the same issue. Many credit card companies have said that they will give Debit Card users the same protection as Credit Cards ($50 fraud, immediate refund of money if fraud is suspected). Don't know if you can hold CC companies, by law, to these rules. Whoever last holds the "check" generally looses the money and it can take a long time for the customer to get money back into their checking about even if fraud is proven and the bank was somewhat responsible (forged check, no ID, etc.).
Pay Pal: No government laws, no regulatory authority. No ability to appeal issues past Pay Pal's own processes/people. They can change their rules anytime. They can close accounts, they can freeze your money, etc. The only rules are Pay Pals rules. If you link their accounts to your checking account, they can sweep money out of your account--and you have to deal with your bank to try and get it back. If you link their account to your CC account--you can appeal through the CC company to get your money back--although--it appears that Pay Pal will hate you for the rest of your life (I guess they will make it hard for you to ever use Pay Pal again?).
Over time, any type of account is vulnerable to fraud (even carrying/paying with cash and checks has issues too). Credit Card transactions seem to offer the best protection for the customer/buyer if something goes wrong. Obviously, improper use of Credit Cards can bury people in debt--a very bad thing in itself. Don't use a CC's revolving credit function--it is a bad deal all the way around (expensive to borrow money, laws are against you if trying to declare bankruptcy).
So, I only use ATM Card (like at local gas station or very major store) when I don't have cash or they don't take Credit Cards. Use Credit Cards everywhere for protection (cash back, airline miles--if you have that) and only use them like checks (have cash to pay off bill every month).
Use checks for bills (or online bill pay now).
Never use Pay Pal or link to my checking account.
I realize that there are literally 10's of millions of people, with probably billions of transactions, that are perfectly happy with Pay Pal (maybe other than their fees) and have never had any problems with Pay Pal.
No expert--but that is how I see it.
-Bill