In any case, as the question states, which of the characters (thinking broadly) do you think would try to date you assuming you didn't pursue them first. What would their first impression be of you, and would they push beyond that first impression?
I'll retread my own comments on the matter here:
I think my crude sarcasm and flippant mocking would infuriate Lilly. Where she's the epitome of tact, I'm the exact opposite. She's also on her way to becoming a raving alcoholic, and I don't drink. Then again opposites attract, and I'm really more of a smart-ass than a crude brute, so you never know.
Emi would try to get me to go outside, work out, or some other such nonsense, and I'd have none of that. I'm also fairly resilient when it comes to pouting - maintaining my objectivity even under the gaze of a DefCon 1 puppy-face is an acquired skill. If she went thermonuclear on me, I might crack, though. I think that would be an automatic friend-zone, though.
I'm not sure if Rin would have the attention span to try and crack through my outer defenses to get to know me. I can be pretty harsh at first meetings, and she might decide it's not worth the effort before it ever got anywhere. I'd have to catch on pretty quick and decide to reciprocate the interest if it were given.
Shizune would certainly have the persistence to dig through that outer defense, and she'd find a willing adversary once the communication wall came down. I think she'd probably have the best chance to do so out of any of the girls - largely because she'd never be able to hear my groaning protests. I'm also a sucker for glasses, which would probably reduce the amount of digging she had to do.
I don't think Hanako would have much chance of approaching anyone considering the state she's in at the beginning of the game. However, as the story arcs, she becomes less awkward and might decide to introduce herself to the calm, quiet guy. I'd also be much less likely to try pushing her away seeing a kindred spirit of sorts.
I imagine I'd develop a sore welt on my shoulder after being punched in the arm daily by Miki. I doubt she'd pursue me romantically, but she'd probably try and figure out what 'makes me tick'. I'm mysterious like that, at times. Usually without my knowing.