A Y-DNA 37 test would be best for you, although the 25 marker test would probably prove it. You can go to www.familytreedna.com and (in upper right box) search Bartlett: click on the project and scroll down to the ordering section. The Y-DNA test is like a laser beam on your all-male line. It's best for what you want to prove.
Because of your rich Colonial ancestry, you may also be interested in the family finder DNA test (google: family finder wiki). This test reports back your cousins from any/all of your ancestors, along any path, and gives their emails. Like all DNA tests, you need to contact them and share ancestry info to determine your Common Ancestors. So far I've confirmed over 70 new cousins (3rd to 10th) with this test. You can order this test at the same place as the Y-DNA test.