I have the biggest problem with big servers. If I can get most points into a rally and find a rhythm, I'm going to have an enjoyable match, even if I lose.
So their serve is the biggest thing I try to find out about early on. After that, I look at how good they are at overall consistency, if they have trouble handling pace or lack thereof, and then individual strokes to pick on.
Basically I try to compare my strengths/weaknesses to their strengths/weaknesses to see what I can use against them. Things like their fitness and mental strength will show themselves during the course of the match.