This is likely to change with the new XP, but my experience so far:
If you go to Gamespy for a opponents, people mostly play Simultaneous. Its faster and more involved than turn based, so you get farther in casual 'pick-up' games. I've had a couple very intersting games this way, a few more lame ones, and many hours of failed attempts to launch games and configure my firewall. The Gamespy lobby is annoyingly noisy and games often aren't actually the type shown on the screen. For the beginner though, this is a quick way to get a feel for the experience. If you only have two hours, you could get a good chunk of a game in.
I don't know what turnless is like to play, but simul already has enough annoying glitches so I'm not looking to explore it.
I haven't found anyone yet who wanted to play turn-based, but this is pretty much accelerated PBEM, you just have to sit around micromanaging or negotiating most of the time. The catch to this type is having a number of players coordinate their schedule to be online at the same time. Turn-based would be the closest to the SP experience, although PBEM isn't that far off.
(You have PBEM in the poll, but don't mention it in your post?)
PBEM is the easiest way to find good opponents. It's the favorite of Apoly-goers (the MP section here sees little action beyond the one-on-one league). Having as long as you want to look over each turn makes the games very different from online. It's...just....so.....very......slooooow. If you have a couple years to play a game and don't mind the chance it will crash halfway there, it's the way to go.
For the full experience, I'm trying to get a game combining PBEM with some turn-based sessions to move things along while keeping interest up. You can switch from an online version to PBEM, but converting back to online again is still unproven.
More info at Hybrid Playtesters Wanted