I just provided a man with this answer about how to use dna for genealogy when you are adopted.
There are 3 tests that are useful for genealogy. I can generally recommend two of them for those who are male, adopted and don't know anything to start. (but a current sale does mean that it's a good time for you to get all three)
So first - order your test(s): I suggest you use your surname as basis for the project you join. (I know that is very unlikely to be where your matches are - but you will get a discount on your yDNA test by ordering through a project) As your surname is one of the names in the project - you shouldn't get any static from the surname project administrator - even though you are adopted. (Note: most projects don't require you identify your ancestry to join - but some do)
Or - if you wish, you can order your test through the "Adopted" project - which is open to anyone.
yDNA: The most useful test for you should be the yDNA test - which is often called the "surname DNA test". This test is for males only. This is your father's father's ... father's paternal line. Your yDNA matches will share a common paternal ancestor with your biological father. If you are like most folks - you'll find that your matches are clustered on a single surname or a surname with spelling variations. (You'll probably also see some additional surnames represented in your matches, which will be a second priority behind the dominating name(s).)
You will ultimately need to be tested at 67 markers ($238 + s/h) as you seek your paternal ancestral connections, but if cash flow is an issue, you can order 37 yDNA now ($149 + s/h) and upgrade ($99) to 67yDNA later - reusing your initial sample. (s/h is $4 domestically and $8 internationally)
atDNA: This will probably be the second most useful test for you. The autosomal block (atDNA) test at FamilyTreeDNA.com is called "Family Finder". This is the "whole family" test and is for both males and females. It is best for your ancestors within the last 5 generations, but will still identify many cousins who are more distant. You will be interested in your "Close and Immediate" matches and will probably be frustrated by your more distant matches. (The standard usage for this test is to find cousins further back than the ones you know by first matching surname and then finding paper trail connections - which won't work very well for you.) You will be hoping to find close matches who can help you zero in on your birth family. Generally, folks using dna for genealogy are nice - so your matches will probably be helpful when they can - even though they are unlikely to gain anything useful to them (other than finding a nice cousin)
There is currently only one level of this test at www.familytreedna.com. Family Finder is $289 + s/h. You can order this test in combination with yDNA or mtDNA if you wish.
NOTE: FTDNA currently has a sale where you can add either yDNA or mtDNA for $10 if you order it as a part of your Family Finder test. One possibility would be to order the Family Finder + a 12 marker yDNA test for $299 + s/h and then immediately upgrade the yDNA to 37 markers for another $99. Another possibility would be to add the basic mtDNA test to Family Finder - also for $299 + s/h
mtDNA: This is probably the least likely to be useful to you - but its very specific insight can be helpful in confirming your birth mother in some circumstances. This test is also for males or females - as each of us receives our mtDNA from our birth mother - who got her mtDNA from her birth mother ... This test only provides insight on your mother's mother's ... mother's maternal ancestry - so its main use will be when you can identify your own mtDNA and the mtDNA relative of your presumed birth mother - when she is not available to test. (If she or your birth father are available to test - and are willing - then a traditional paternity test - not discussed here - would become your choice for ultimate confirmation)
There are three levels of mtDNA testing. The basic - or low resolution - mtDNA test (also called HVR1) is $99 +s/h when purchased alone and $89 when added as an upgrade to another dna test - using your existing sample. The third level of mtDNA test is called "Full Sequence" and is $289 as an upgrade to a yDNA test or $299 as a standalone test. The Full Sequence test may identify only a very few matches (and even sometimes none) - which you will hope are closely enough related to identify your family. (Note: this has a low probability of success). I don't see a good reason to order the middle level - HVR1+2 at $159 for adoptee research.
Second: After you have identified your best matches - you must discern what surname and family insights you have gained and then embark on more traditional searches - using your new insights to reduce the size of your search