Basically, as you have already stated, the Premier account allows you to accept PayPal payments that the buyer makes using their credit card. That gives you a much greater range of buyers who will be willing to buy from you. In exchange, you pay a fee on each transaction.
If you do not have a Premier account, the buyer can only pay you using the checking account that is linked to their PayPal account. That is, when they pay you, it is debited directly from their checking account instead of from a credit card.
The basic service is free, but, of course, you'll not be able to take payments from buyers who wish to use their credit card.
Which is better for you depends on how much you intend to sell on eBay and how big of a pool of potential buyers you want. If you are only occasionally selling things, you can probably stick with the basic account. But if you start selling a lot of stuff, you may wish to upgrade to Premier.
Here's what you can do (and what I did)... stick with the basic account until someone actually attempts to pay for the transaction with their credit card. Then, when someone does, PayPal will send you a notice giving you the option of upgrading to the Premier account (and thereby accepting the buyer's credit card payment), or denying the credit card payment and requesting the payment be made from the buyer's checking account.
However, if you decide you want to stick with the free basic account, you may wish to indicate in your auction description that you only accept PayPal payments made from the buyer's checking account.
Hope this helps. Good luck!