I personally think it is a good idea to offer BOTH Paypal and another option for processing credit cards. Some people who shop online a lot are used to Paypal and like to use it especially if they have a current balance. Other people who don't shop online as much can get a little turned off by Paypal and the way it is set up.
Many shopping carts will allow you to offer both options.
Anyway, you will need to get a merchant account and a payment gateway. You can do a google search and compare rates. I personally signed up through Secure Net
and it had no set up fee which I liked.
I highly suggest making your choices and getting this ready ahead of time. I started with Paypal only and now am having a difficult time integrating my credit card processing with my custom shopping cart. It might be worth looking into getting a shopping cart that is compatible with the credit card processing you chose.
If I had it to do all over again, I think I might use Mal's Shopping Cart
with Authorize.Net as the payment gateway.