Ok, I'm adding my $0.02... And as I'm currently looking for a stud, I'll just use my current situation as an example.
First thing, I like to look at bloodlines. I usually have an idea of what kind of lines I want and what kind I don't want (and what kind I know are good, but maybe not necessarily what I want at the time). (For instance, my mare is OLD speed bred, and I'd like to find something along those lines, but I doubt it, since she's so old (well, within my budget and other restraints) so I know what I think would make a good cross on her and I weed out the rest.)
Secondly, I look at conformation. (Well, these 2 are actually interchangable kind of.) I check to make sure he's built properly, athletically, and would fill out my mare's weak spots. (She has a high wither, so a nice topline really goes well on her.) I also like to look at some of the stud's get to see how THEY are built.
Finally, I want a nice disposition. (Again, I suppose sort of interchangable with the first two -- in the sense that all 3 must be met.) Puppy dog like. I've owned my share of studs, and I know that most of the time, if they pass on NOTHING else, they pass on their disposition!
And finally, such as in this particular instance, I want a palomino, so since I've found out that a cremello will guarantee me that, I have started my search with color (which usually isn't even on my list to consider, but this time it's different). However, I only *start* with the color, and then the stud has to match the above criteria... Let's just say this has been one of the hardest searches in my life! [confused]