Let me give a disclaimer first, I am not a DNA expert, I am a believer. I can't tell you a lot of technical things but I can tell you that it is very interesting to understand who you really are. It may be shocking or it may be exactly what you expect but either way, it is fascinating stuff.
I first had my DNA analyzed years ago. In those days all women could do was mitochondrial DNA. This is what you inherit from your mother and her mother and her mother back to your deep ancestors. If you never have, I suggest you read The Seven Daughters of Eve by Bryan Sykes. It is fascinating. It breaks down modern Europeans into seven groups, the mitochondrial haplogroups. These groups have female names Ursula (U), Xenia (X), Helena (H), Velda (V), Tara (T), Katrine (K)and Jasmine (J). I so wanted to be in Helena's group.
My friends know exactly what I did find. I am none of the above. The good news is, my husband is an H so he descends from Helena. I on the other hand am a C haplogroup, C maybe for Cochise. I am a Native American. I know strange isn't it. Actually I am less than 1% Native American going by my Autosomal DNA but that is for another post.
In short, mitochondrial DNA is how they identified both Tsar Nicholas and King Richard III. It is good for telling you your deep ancestry. But, sons only carry this from their mother for one generation and they do not pass it on to their children, only mothers pass it on. So, it might be worthwhile to do this test.
For men, Y testing is very accurate and it can help identify which branch of a family you are descended from. I was able to determine that we are the Royal Donahue's which is not a bad thing to know, lol. I had my nephew do this test for me.
This is just a very little bit of information about DNA and how it can help you with your genealogy. It does not however take the place of research, it just is a tool that can help rule something in or out.
Unless you are only interested in your nationality, don't purchase autosomal first, you can always get it later like I did.There are several places to purchase these kits. I can't recommend a place for the Mito or Y since I had mine done by Sorensen and they no longer are doing tests and have been acquired by Ancestry.com