I recommend using the testing firm Family Tree DNA, based in Houston, Texas.
It has built up the most comprehensive databases of results of any of the firms marketing genetic tests to genealogists, which means that when your results come through you have the best chance of finding a connection among other testees.
It hosts the vast majority of all registered Y-chromosome surname projects worldwide.
And it offers a range of tests which investigate different relationships in our family tree, including the male line Y-chromosome test, the female line mitochondrial DNA test, and the 'close ancestry' Family Finder test which seeks to identify anyone who shares a relation with you in the past five generations.
With the Family Finder and mitochondrial tests you can just go ahead and order a test. To find a match with someone else's result you'll be relying on the company database to identify them and alert you.
With the Y-chromosome test there's a huge advantage if you check before you order a test kit to see if there's a project already registered for your surname. You can do that using the special search box on the right hand side of the standard FTDNA page. If you rely on the company's database to find a result match it will only ever show you other people who match your own result almost exactly. But within a surname project the project administrator will be able to see the results of everyone within the project, which will include those name bearers with DNA results different from your own. This is extremely useful if you yourself want to co-ordinate the collection of DNA results with the analysis of participants' family trees. To do that you need to see the big picture, which you can only do within a whole surname project.
Don't worry if your surname is included in another project as the project administrator will still be able to compare the results of men with your specific surname. What is important is that you join a project that is organised around a surname, or group of surnames, rather than a place or tribe. There is a mechanism once you've signed up within a surname project to join any other non-surname project you wish, but it's important to join the most appropriate surname project from the outset. If no surname project exists for your surname, go ahead and register one yourself. There's no obligation for you to do any extra work and you may well find other people joining later who can help your research even if your DNA results are different.
Note also that the price of a Y-chromosome kit is always lower when you order it as a member of a Y-chromosome project than if you order it from the main page as an individual.
View all of Family Tree DNA's Products & Prices.