Go with LOST. There's no better time to dive into it ... the 8-month hiatus is perfect for catching up with all 3 seasons thus far, without the need to do huge marathons to cram it in in time. Seasons 1 and 2 are out on DVD already and Season 3 is expected to hit shelves mid-september. The ironic thing, though, is that once you start watching you probably WILL want to do those marathons.

Out of those I pick Lost... but if you like Joss Whedon's stuff (well written fantasy that doesn't take itself too seriously) check out the new Doctor Who series.

The Wire
Rome
The Shield
Lost
Weeds (the only one I haven't seen)

I don't think Lost compares to any other show. It's a complete mind fuck.

Lost.

I love Lost. But FWIW, note TheGodfather's comment. Lost is on network TV and is watched by a lot of people. Many people voting in your poll haven't even seen The Wire.

LOST has too much filler. Wait until it ends to see if it's worth the time. THE SHIELD ends next year but has been pretty riveting all its run.

I disagree with the filler comment on Lost, thought it's had a pretty brisk pace through most of seasons 1 and 3 with some occasional filler clogging season 2, no better time to start imo. Plus it has a similar vibe to Twin Peaks in spots.

That said, my votes go to Lost, The Wire, and Boston Legal (Underrated comedic gold).

I've enjoyed The Shield from time to time but always felt it could be a lot better (Which oddly is my feeling toward several FX shows, but at least they're trying.)

Since no one has mentioned it, The West Wing

Watch Lost season 1-3 a few weeks before season 4 starts. This way you don't have to wait long to see what happens next. I hate waiting on more Lost.

The Shield is my favorite of all the others listed so I say go with that first.

Maybe "Twilight Zone," but with an ongoing story?

Judge Judy

the wire (with rome being a close second).

What was the point in the poll?

Of the ones you listed, I'd go with Rome, followed by Weeds. I haven't seen the Wire or the Shield, though I hear great things about both.

I'll second the recommendation for Doctor Who. Start with Season One of the revival and don't be intimidated by the fact that it's a restart of a series that ran for thirty years -- it's totally newbie friendly.

Others that you didn't mention that are worth checking out:
Dead Like Me
Carnivale (if you can live with the fact that it ends on what is really just the end of the first act -- but it's such a great first act that it's worth watching)
Deadwood
Scrubs

Scrubs is already listed so I thing you should watch...

The Larry Sanders Show

I love Lost; I'm totally addicted to it. The Wire is excellent, but I just never really got that into it.

you gotta start watching lost.

Weeds or Dexter.

I envy you for starting that journey for the first time. Simply the best that television can be, although The Wire is a close second. Might wanna check out Huff and Dexter also if you haven't.