I too have been single for a while. A relationship a few years ago left me pretty hurt, and I have been so picky about what I get in to since that. 
I think attraction is very important initially, for me at least. But there have been a few guys that I have grown to like more than just friends after getting to know more about the person they are and how we act together. And that has really suprised me. 
Sophomore year, a semester after a hard breakup, I was a student advisor to the res hall floor below mine. To sum it up, I met one of the residents through a fraternity mixer and we ended up walking home from the function together talking the whole night and joking about how people might think we were hooking up. 
Well, we ended up talking each day and several times after and becoming better friends, but I never felt anything more than just friendship. He felt different and told my friends that. 
So finally, I start to see him in a different light and we go out together for a weekend. Then it became really weird, and we just decided to be friends. So I have become attracted to someone after having a friendship firs, but the minute I saw him differently our friendship skewed.
At the same time, there have also been (two) recently guys that I have gone out with and have a good conversation with, but the physical attraction isn't there and never really developed.
I don't think theres anything wrong with being picky, at the same time you need to just follow how you feel. But always keep your standards high.