Marianne,
If your purpose is to have your "ancestry painting", for example if you think you might have non-Greek ancestrors but aren't sure about it, the test you should take is an autosomal DNA test, such as the one offered by 23andme. This is currently the best value test because it tests a bit of each chromosome + mitochondrial DNA. What you will get is :
- your mtDNA haplogroup (+Y-DNA for men)
- ancestry painting showing where you stand on a virtual map of Europe (so if you are half Greek and half Finn, to use your example, you will be half-way between Finns and Greeks).
- your health profile, including risks for various genetic diseases, but also informative traits. You can see a non-exhaustive list of mutations tested by 23andMe in the genetic section.
- you can also compare the percentage of similarity for selected traits with your family and friends (or anybody you choose to share your data with).
- you can compare family inheritance of chromosome sections. If you have a doubt about your brother being your brother, for instance, you can be sure by comparing this.
The main interest of Y-DNA tests is not to know one's detailed ancestry (it's only one line out of millions), but rather to understand better historical migrations and the overall composition of a targeted population. It's interesting to know which ancient ethnic groups merged to make the present population of a country or region. Inside Greece, if your ancestors all come from one specific region, you can know that the genetic make-up of that region is quite different from another region. For instance Crete has a lot of J2 and little R1a, while it is the opposite in Macedonia.