I prefer to get standard def reference videos, things just tend to run smoother in tools that way. I'd suggest trying to stay away from any HD codecs. I do like them to include their "mix" when they export the reference video, because I'll pull that in as a reference within my session.
I always request pops at head and tail, this is usually best presented as making things easier for the editor. If you send back the final mix with pops, they have a fast and easy way to initially verify sync when they drop it back into the timeline. I do ask for large handles, minimum of 5 seconds (especially if the omf is coming from a Final Cut system), unless the omf they're exporting references the original files (rather than contains them). Final Cut can't reference original media from an OMF, it will only consolidate regions. So, don't forget those handles.
If the editor does any organization of the omf it does make life a little easier, but I always end up reorganizing it anyways. I open the omf, copy/duplicate all of the tracks and hide the originals from the omf. Hiding the originals saves the layout in case I royally screw something up. Working with those copies, I then move the audio files around as I'd like to have them: dialogue over several tracks, production/ambience, hard effects, music, etc. Once I have everything split out. I duplicate the playlists, save and close the session.
I'll create new sessions for each of my tasks, and import the respective tracks (copying all source audio files). So, I'll import only dialogue tracks from my omf configuration session into my dialogue edit session. Now I'm working with copies of the original files, because some of the things I do can be destructive/permanently change the waveform (like the pencil tool). I'm also working off the duplicated playlist that I created in the omf session; again, so the layout is saved on a previous playlist in case I screw something up. Redundant backups and ways to quickly correct a bad decision are goods thing. And we all need them sooner or later.
On longer form projects, I prefer reels. I say that, because they may lock a section of the picture well before the whole is done. No reason I should wait until the whole project is done before I start working on sections of it. That just seems inefficient to me. There are plenty of times though when I get brought in at the last minute; in that case, I'm usually getting one big one. This is all really up to what you work out with the director/producer. Go with whatever workflow is going to be more efficient for the project.
I don't ever ask the editor to do any work. If they choose to that's fine. I'm not going to step on any toes by telling them not to, but I don't request it. I discard all fades, crossfades, pan and volume automation the omfs contain. I have the reference audio track that I can listen to for that information if I'm confused by something.
I haven't ever worked on a project that had money for anyone other than the editor to conduct media management, and they usually only have time to organize things in a way that makes sense for them while editing. There's usually a fair bit of logic in that though, so I don't think of it as a handicap. I do request any logging data or sound reports that might be available. I'll usually ask for an EDL as well. This is a must if the omf is going to come from Final Cut, because FCP creates new metadata for the files it includes in the omf. Without and EDL, you'll have no idea where a clip came from if you need an alternate take or some other piece of audio. Those documents have covered most of my needs in the past.