Cost is certainly a major consideration. Another is a CFI's ability to teach me the things I need to know to be a safe pilot. I'm able to get along with most people so I'm not as concerned as others might be with making sure personalities "match." As long as the CFI can help me learn that that I need to know I'll probably work just fine with him. If for some reason it doesn't work out I'll find another CFI.
Kevin
Kevin