A merchant account allows you to accept credit card payments from your customers and have the funds deposited into your banking account. You apply with companies that have relationships with processing banks. These processing banks do the work that gets you paid for your sales.
Accepting credit cards does have a cost to it. Typically a small percentage of your sale plus a small flat fee is charged for accepting a credit card payment. This amount is usually around 2% of the transaction's value +/- .5%. There is also usually a monthly fee associated with having a merchant account and this is typically $10.
Other fees that you want to avoid are: monthly minimum fee, set up, application fees, annual fees, and also make sure you are not locked into a contract. AVS should be included and should not cost an extra fee.
To process your transactions you will need a credit card terminal of some kind. The kind you will need will depend on how you plan to physically process your sales. If you can bring your credit card terminal with you to each party and have access to a telephone line and electricity you have a lot of choices available to you. I would recommend the Verifone Omni 3730 LE. It is small and easy ported and has the latest and greatest features built in.
If you can bring your terminal with you but won't have a telephone line or electricity then a wireless terminal may work for you. The Nurit 8000 is probably the best wireless terminal out there. Just keep in mind this option is more expensive then a regular terminal.
If you can't bring a terminal with you then use a manual imprinter to capture all of your sales and bring them back to a basic terminal at your home or office. Manual imprinters are very inexpensive and the terminals you can use with them are as well because they don't have a printer built in (you don't need one). I would recommend the Verifone Tranz 380 as it is small, easy to use, and very affordable.
As far as choosing a provider, well, there are a ton of them out there. I definitely recommending shopping around as the more you look the better the rates seem to get. I've linked to a comparison worksheet that should make this a lot easier for you to do.