If your family has been in the U.S.A. since the 1700s, that would imply that they are Americans.
As to Arkansas history, see: http://littlerock.about.com/cs/generalhistory/a/settlers.htm
So you are talking about being in Arkansas before it was even a territory!
As to which whites were in what is now the U.S. of A. back then, there were first the Spaniards, then the French. Of course, the Brits hung out along the Atlantic Coast at first; don't forget the Netherlanders founded New Holland (now New York).
While searching for my ancestors in Virginia in the late 1700s, I noticed that the various names included Chinese names. (These ancestors of mine were mostly of German extraction, but also Swiss and English).
So, white settlers would have included Spaniards, French, English, Netherlanders, Belgiums, Austrians, Swiss, Germans and just about any others from Western Europe.
To find out what YOUR ancesters were, what countries they were from, you will need to do the research, starting with:
You should start by asking all your living relatives about family history. Then, armed with that information, you can go to your public library and check to see if it has a genealogy department. Most do nowadays; also, don't forget to check at community colleges, universities, etc. Our public library has both www.ancestry.com and www.heritagequest.com free for anyone to use (no library card required).
Another place to check out is any of the Mormon's Family History Centers. They allow people to search for their family history (and, NO, they don't try to convert you).
A third option is one of the following websites:
http://www.searchforancestors.com/...
http://www.censusrecords.net/?o_xid=2739...
www dot usgenweb dot com/
www dot census dot gov/
http://www.rootsweb.com/
www dot ukgenweb dot com/
www dot archives dot gov/
http://www.familysearch.org/
http://www.accessgenealogy.com/...
http://www.cyndislist.com/
www dot geni dot com/
Cyndi's has the most links to genealogy websites, whether ship's passenger lists, ancestors from Africa, ancestors from the Philippines, where ever and whatever.
Of course, you may be successful by googling: "john doe, born 1620, plimouth, massachusetts" as an example.
Good luck and have fun!
Check out this article on five great free genealogy websites:
www dot associatedcontent dot com/article...
Then there is the DNA test; if you decide you want to REALLY know where your ancestors came from opt for the DNA test. Besides all the mistakes that officials commonly make, from 10% to 20% of birth certificates list the father wrong; that is, mama was doing the hanky-panky and someone else was the REAL father. That won't show up on the internet or in books; it WILL show up in DNA.
I used www.familytreedna.com which works with the National Geographics Genotype Program.