PayPal is a payment service owned and operated by eBay. Great for buyers, not so great for sellers. There are many safeguards put in place for buyers, and is perfectly safe in my experience. If you're looking just to purchase items on eBay, PayPal is your only choice. It could take up to a week to register an account though, as you need to verify your bank account with them in order to transfer funds.
Most shopping websites would rather you just entered your debit/credit card details, but as you lack the facility you'll need to hunt around for trustworthy PayPal secured sites. I'd stick with eBay, if I were you.