That's an unfortuneate price range. The best buys are in the $700-900 and $1600-2000 ranges. There is a significant void between the two right now.
If your budget is "up to $1,200," then I would suggest getting one of the $700-$900 guns, and spend the rest on
quality magazines (about $100 for 5 Chip McCormick's), ammo, and holster and training (depending on your experience level and intended use).
Based on my browsing gun shops in my area, $700 - $900 would get you a 1911 by any reputable manufacturer: Colt, Kimber, Para Ordnance, Sig, Springfield, Smith & Wesson, etc.
Actual "street price" will vary depending on your geographic location, and specific dealer. But I find that
BudsGunShop.com and
eBang.com are good web sites to get a general idea of price. Keep in mind that eBang also lists on-going auctions, so some of the prices listed will be current bids, not the actual sale price.
The differences between the above-listed manufacturers are probably so minor that 1911 aficionados and internet commandos will spend countless hours passionately debating why their choice is better. In the end, it may simply come down to availability, style, and some intangibles.
The only modification
I would do to any of those guns in that price range is have a brass bead front sight installed, about $40 parts and labor at my local gun smith.
UPDATE: I see that you are in New York City, which may change things considerably, given the regulation-imposed costs of gun ownership in that area.