Well - the 3GB 580 is the way to go for mulitple monitors spread across three screens IMO. You'll also be thinking ahead should gaming get more VRAM intensive.
Remember VRAM is mirroed not added together, in case you didn't know that. So even if you have two 2GB cards, your not utilizing 4GB's of VRAM but still only 2GB. Having the extra 1GB VRAM will go a longer way and increase performance on multiples.
Only in single monitor situations will there be no difference between 1.5GB or 3GB in performance FPS.
Though true currently it's a bit high priced and price/performance you can get a lesser GPU, you also leave the door open to having two 580's 3GB.
Currently, I'm running one 580 1.5GB with games maxed out just fine. Metro 2033 is the only game maxed out on single 1080p monitor (though it's playable) is less than 60 FPS.
BF3 as you can see on one stock 580 is getting a tad over 60 FPS on High settings with one 1920x1080p monitor. In six months when you looking into a second monitor the 3GB card will do nicley as opposed to spreading 2GB across two monitors.
Pricing will also have dropped in 6 months anyway because the next gen cards will be out and have time to saturate the market and the price of 580's will be less.
The only reason not to go with the 580 3GB is if you don't have the cash or plan on getting 3 monitors with one card. If so, Nvidia can only run 2 monitors with one card. You'll need that second card to run three.
Just giving you some food for thought. The other suggestions prior are all good really. 2GB VRAM from any cards will do if SLI'd or Crossfired across three monitors.
The Zotac GTX580 3GB
your thinking about is a good card. I've heard some good things about Zotac and nothing negative. A lot of OCN members who have them love them. On the 580 Overclock club they do rather nicely as well.
I personally have enjoyed the 580 as a strong single GPU solution for my single 1080p monitor. Simple, and haven't had any issues since installing in January. None. Been running a 13% over clock since, on stock voltage 1.0880 24/7 and a 20% bump for gaming with 1.100v.
Oh btw mhansen23, Welcome to OCN fellow Arizonian.
Update us and post back when you've pulled the trigger. Good luck.