#1
Belief in God, but a willingness to ask questions about him.
This is my most important criteria, and the only requirement. The explanation goes into Zephyrin's comment about having a common interest, for me this is my most important interest and the one concept in my life philosophy that doesn't change. If we can't agree on it then my decisions and modus operandi will cause major conflict even if I don't (and I never have) set out to make him agree. If we have that, we can find common ground on anything. Blind faith, though, is an untested one, and I don't want him to fall apart on me when he discovers what science has learned.
#2
Lust.
(... for life, though a healthy libido is good.) Perhaps passion would be a better word. It's a big world out there, I want to explore it and learn about it. It's important that he want to come with me. Even if his interests are narrow he must have some spark in him that makes life interesting. Few things are as unattractive to me as apathy.
#3
Cleanliness.
Personal hygiene is very important. It doesn't matter so much whether he's handsome, but I have a very sensitive sense of smell and an aversion to unkempt hair that can be very distracting.
Once those three are met, the rest is a matter of patience and open-mindedness, and I can work with it. He doesn't have to be brilliant, it would be nice to have a clever spouse but my need for conversation doesn't have to be met by him exclusively. Neither does he need to meet all my material or emotional needs, in fact, I'd prefer not to rely on any one person for those. Some things that I'd find attractive, but don't necessarily need are long hair, a fit body, winsome personality, ability to sympathize, an understanding of programming, math geekery, strong personality, and sense of direction in life.
Jam it back in, in the dark.