I wouldn't consider PayPal a valid form of payment for anything online. I'm interested in paying for whatever it is I'm buying, not getting stuck with an account that I'm never going to use and that I will get spammed for to maintain every two months.
As long as PayPal couples it's service to a required signup for an account, I'm just going to look elsewhere for the same product.
As far as hosting goes, I'd consider a host with a third party processor over one that handles payment themselves. If there's a dispute about charges, or if the host goes out of business, there's noone else left to negotiate with.
When I cancelled with my first host ever, they kept saying they refunded but never actually did; forwarding all of the conversation to the third party processor eventually made them withdraw the funds from the host's account and refund my credit card.
On the flip side, one host I'm currently with now switched from third party to handling it by themselves. Instead of blanking out everything except 4 or 8 digits of the card number, my card number is there in its full glory along with expiration date and full address. Hardly something that makes me feel secure.