A large topic, to be sure.
I guess the basic question I would have for you is, "what is a friend for you?"
A seemingly easy question to answer, yet people have been writing about it in the West since Aristotle. Aristotle himself said that there are several types of friendships, but the one that is the rarest is the one in which two people see, appreciate and actually enjoy something about one another. The other types of friendships are a bit more "superficial", literally, based mostly on tit-for-tat, I'll be you're friend but what do I get out of it? kinda notions.
This rationale could apply to any kind of relationship between two people, and in this particular case you're interested in finding a man who would be interested in you and vice versa (and not just for sex). A lot of men (and women too) ARE looking for just sex, so it seems, and we can say that without attaching a negative connotation to it. You are also quite young, and so a lot of men you're most likely running into are making a lot of "beginner's mistakes". Life is about processing and learning, right?
So, cue Aristotle (inserts him a la Deus ex Machina-style): it may very well be a fact that the type of relationship you are looking for is quite rare among any two people of any gender and any sexual orientation. Most of what you will encounter will not be what you're looking for, then. However, the bright side of the coin is that since you do in fact know what kind of relationship you want with a man, you're miles ahead of many men who spend their whole lives relatively clueless about what they really want (we've all seen it over and over again). Be true to yourself, relax, have patience, and since as another famous Greek said, "like attracts like", you may very well end up meeting a man at some point on your path about whom you'll think "I could see myself in a relationship with him", and he may very well think the same about you.
Hope this helps; I hadn't ever thought I might actually put long-dead white men's words to good use, but I think they may be right on. Good luck!