Genealogy Questions? Ask a Genealogist for Answers ASAP
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If you want to get this done, the cheapest testing is under $100, while better tests are in the $200 to $300 ball park.
However, and this is a BIG however, it does NOT do your family tree for you. The cheap ones just tell you that you are possibly 25% African, 25% Scandanavian, etc. Others give more information, but they do NOT tell you who your great-grandparents, great-great-grandparents, etc. were. So if what you want to determine is your family tree, then you will need to do the genealogy research.
Cheapest isn't best. FamilyTreeDNA has one for just $79. Others start at $99 (AncestryDNA) and go upward from there.
The largest free family search site is www.familysearch.org. The other free ones aren't worth the time you spend looking at them. Occasionally ancestry.com will offer a free 2-week trial.
Just be sure to ignore all the things that are put online by other "researchers." I've seen too many cases of 4 year-old girls giving birth and grandsons fathering their grandfathers. So by all means use their records (censuses, etc), but ignore the other stuff.