This is under your budget but for you I would go with a 27 in 1440p korean monitor paired with a gtx 980. The combination should cost you around $1000. Below I've got some info on korean monitors for you.
There are korean monitors sold on ebay that are really great. Basically, they take the screens from Apple or Samsung that are graded at like an A- and put them in their own housing. They are still great screens but don't meet apple's strict standard. So basically you get a screen that has a value closer to $800-$1100 for $250-$400. It's definitely worth looking into.
Below the first link has a list of the best Korean monitors and the best vendors according to Tek Syndicate. The second link is a youtube video about korean monitors you should check out. I would highly recommend you at least consider going this route. If you look into and decide it's not for you that's fine, but don't miss an opportunity you weren't aware of.
https://teksyndicate.com/news/2013/08/15/tek-syndicate-...
https://www.youtube.com/watch?v=5rQtubyNCQA
Instead of looking at 1440p you can look at 1080p with a high refresh rate like 144 Hz instead of 60 Hz. Some people, especially people who are really into FPS games, are all about the frame rate. I would rather play a game between 40-60 frames per second on the highest possible settings however. If you want games to look their best, go with one of the 1440p korean monitors. If you want an edge in FPS games and are willing to take a hit to the eye candy, go 1080p with a high refresh rate from BenQ or some similar brand.
Now that I have gone 1440p with my GTX 770 4 GB in SLI I will never go back to 1080p.
Good luck on your search! Let me know if you have any questions about this.