I ordered DNA tests from Family Tree DNA. I used them because I feel their privacy statement is the strongest, and because their tests are more extensive than Ancestry or 23andMe. There are some other testing companies that are less well known.
I don't have my results yet and am waiting impatiently.
I'm not at all interested in learning what my ethnic makeup is. Two of my grandparents got off the boat from Lithuania, and on the other side of the family three great-grandparents got off the boat from Germany. That leaves only one great-grandparent and her ancestry has been thoroughly traced. So I know my ethnic makeup (unless there was what genetic genealogists call a "non paternal event").
There are basically three kinds of DNA results. One is Y DNA, for which only men can be tested. Your Y DNA tells who your father's father's father (etc) was. The Y DNA is passed intact from great grandfather to grandfather to father to son.
The second type is mt (mitochondrial) DNA. Both men and women can be tested for mt DNA, but it is passed from mother to child. So it will tell who your mother's mother's mother (etc) was. Both sons and daughters inherit their mt DNA from their mothers, but men do not pass it to their children.
The third type is au (autosomal) DNA. Everyone gets a mixture of au DNA from both their parents. Siblings will not have the same autosomal DNA, though it will probably be similar.
All the types of DNA can be used to determine how you are related to another person. Y DNA and mt DNA can tell you who your parents are (and your father's father, and your mother's mother), but au DNA can tell you about other relationships.
Since I don't have my results back yet I'm still not certain what I will learn. It depends somewhat on whether there are other individuals in my ancestral tree who have been tested as well.
Many men are extremely interested in their Y DNA because it is "surname" DNA. In theory, everyone with your Y DNA should have the same surname as you. However, in practice you do not all have the same surname, because when the mutation occurred that created your Y DNA, surnames were not yet in use.
I joined the "Baltic Sea Project" on the Family Tree DNA (FTDNA) web site. Right now some of the people are a little excited because a new member seems to be descended from "Gedymin," by which I assume they mean the Grand Duke. I think I know why they believe that, but I'm going to wait to try to figure out more when I have my own results and can do my studying on my results rather than someone else's.
However, my ancestors were peasants so I don't think I am descended from nobility. I'm not sure what my DNA testing will teach me but I'm sure it will be interesting in some way.
NOTE ABOUT ANCESTRY DNA RESULTS: If you have your results, it's a very good idea to load them into GEDMatch. As far as I know, Ancestry doesn't provide you with the tools to do much genealogical investigation with the results you get from them, but GEDMatch does. I can't help you with the use of GEDMatch because I don't yet have results to load into it, but there are a lot of user groups with helpful people.
Genetic genealogy is a whole world beyond regular genealogy and it's very interesting.