Firstly, I want to mention I am a VOLUNTEER administrator for the Dawson DNA Project. The only way I benefit is through potential Dawson matches to my line. And most definitely, the more Dawsons tested benefit all Dawson researchers.
As Neva mentioned, start with the number of YDNA markers you can afford. Some of my family have shared the costs because they were curious too.
When ordering your kit, join only the surname project of the person tested. All marker results are compared to every kit tested, regardless of surname. And if an adoption occurred sometime in your line, you could have significant, multiple matches to another surname. In that case, contact that surname project administrator-your results (markers) could belong in the second project as well.