DNA testing, and it’s uses in genetic genealogy research have come a long way.
There are several good sites to use to have testing done, and even more that provide tools and help with the results of those tests..
For Y-DNA testing (the male only line):
Family Tree DNA is, to me, the best option. You can start ‘small’ testing just 12 markers, and upgrade when you like without having to submit additional samples. You won’t find 12 markers very useful really, but it’s a start. I am not even sure they have that test available now.
For Autosomal DNA testing:
I suggest testing at Ancestry DNA, and then submitting your results to GedMatch (a free service) and transferring a copy to FTDNA as well, which can be done for free, but to get your full match list there you’ll need to pay them. The current price is $39 US.
23&Me is the ‘other’ big name in Autosomal testing, I have not used the service myself yet, but do have a kit in progress there.
Family Tree DNA also offers autosomal testing of their own in addition to allowing you import from other services.