This is really different strokes. Come as you are. Smoke em if you got em. I don't mind "see anything you like" as long as the other owner isn't in a hurry. I usually mull over my trades, and it's going to take me a little longer if I have to look around. I'm going to assume, unless I'm offering something of great value, that the other guy isn't just going to hand over the first best prospect I see.
And I go for win-win. I'm usually trading something different than what I'm getting back. Don't like dealing with guys who are all about just seeing if they can filch your best player.
For that reason I usually hate the unsolicited offer. All the time playing this I've only ever received one unsolicited offer which made me say, "hey that's not a bad idea." Usually it's "here's some stuff I don't really want, can I have something of yours that you want to keep?"
I like trade chat. If I establish a rapport with another owner it can lead to further deals down the road, you get comfortable dealing with a guy and you know his playing style.
Biggest no-no, bait and switch. Happened to me once, early. The guy got me interested in his pitcher, tried to reel in the noob. Said "don't want much, maybe a sandwich pick." I said, look at these two guys, which one do you prefer? He comes back, "huh, they're not that good, I might deal him if I can get both." EFFF YOUUUUU. The two players became my GG CF and best slugger for several seasons.