Hello Christine, If you are wanting to research your father's male lineage the very best company is Family Tree DNA (FTDNA) and the higher the number of markers you can afford to test of the 12-25-37-67-111 yDNA tests you can afford to test the better for your long term research.
FTDNA has a great sale on the yDNA until Dec 31st. If you want to order this is the best time for the next few months for certain.
You want to join a surname group when you order your test. If your brother is a McKee that is the group to begin with and after you have your results you can also join other groups.
Are you related to Ambrose McKee? I would very much enjoy exchanging further info on any McKee and our ongoing and wide ranging research.
One can visit the McKee Group at FTDNA by going to the FTDNA Home page and hover over the tab fro PROJECTS and follow the pages until you arrive at the page to select groups. When you click on the surname you will go to the McKee Home Page, or whatever surname you select, and you can see the members of the project by clicking the tab YDNA results on the Tab bar.