is there a type of credit card where I don't have any additional
charge, i.e., finance charge, when I pay my bill in full each month?

Hi,
Most credit cards include a grace period. A grace period consits of a
set number of days. I you pay your outstanding amounts within the
grace period, you will usually not be charged any finance charge.
Most credit cards have a grace period of 25 days. So if you pay off
your credit card bill within 25 days you usually don't have to pay
anything else.

Some credit cards are completely free; some require an annual fee. 
At www.federalreserve.gov/pubs/shop/shop.txt you can find a list of
credit cards with corresponding annual fees and grace periods (this
list was compiled at July 31st 2003 so the data is quite current). It
also includes contact information.

Remember that APR is the interest rate which you will have to pay over
any outstanding amounts after your grace period and wich will amount
to a possible financial charge.
You would be wise to choose a credit card with a 0 annual fee and a low APR. 
Ofcourse, there might be other factors which could influence your decision. 

Search strategy:
Google: +"credit card" +"finance charge"

I hope you now have enough information. If you need any more, please
ask for a clarification!

Thank you, 
paul_b_18