There are several levels of solution for accepting payments online.
The best solution varies depending on budget. Ideally you accept all major credit cards, plus PayPal. Taking major credit cards gives you credibility, makes you look big. Accepting PayPal gives people an easy solution who may not have a credit or debit card, or who feel uncomfortable giving their card information to someone unknown, no matter how good they look.
If you accept only PayPal you look like a small operation and are less trusted to that degree. But in that case you don’t need a full blown shopping cart as part of your site, if you are only selling one or a couple different items you can just use PayPal “buy now” buttons – very easy and fast to set up, and with no monthly fees to you.