I've used Paypal for quite a long time (ever since they started I believe) and have never had any problems with them.

I prefer to pay for things via Paypal instead of a credit card when I purchase online as your personal details (bank account, card numbers, etc) are not disclosed to the seller.

You also get buyer protection when paying via Paypal, so if an item doesn't arrive or arrives damaged or is not as described, you are able to lodge a claim and in most reasonable cases, you will get a refund (although it is a lengthy and time consuming process).

(FYI, the way I have my account configured, they draw money directly from my bank account (not a debit card) and then I have a credit card listed with them as well as a back up source - this hasn't given me any dramas thus far).

EDIT - and now that you have edited your original post, to answer your question, yes, you can use your Debit (Mastercard or Visa) Card.

They act in the same way as a credit card except that they are drawing on your own personal savings.