Advice for Upgrade (CPU, GPU, Mobo, RAM)

If you have $900 to solely cover cpu/gpu/mobo/ram then you have a lot to play with. Tbh at that price your resolution is kinda irrelevant as you'll have up to $500 to spend on graphics alone which can cover you nicely on pretty much any normal single display.

The i5 3570K is still worth consideration, but as you want this build to last a while it's probably best to jump to the 4670K, it's no faster but runs on a newer platform which offers upgrade potential. Right now there's a bit of a price gap, but it should probably narrow in time. Given your usage, there's probably not much point wasting an additional $100 on an i7 4770k, but it's perhaps worth considering as games like BF4 are beginning to exploit multithreading better.

If you do pick a Haswell (4*** series) processor, I'd recommend looking at the mid-high end motherboards. The super expensive ones are very fancy but don't offer much return on your spending other than aesthetics, niche features and acronyms. The ASRock Z87 Extreme4, Asus Z87-Plus and Gigabyte Z87X-UD3H are all pretty competitive on price and probably offer the best value/features balance. Right now they are priced in the $140-150 bracket.

Ram is pretty simple. You want 8Gb, in 2 sticks, at least 1600Mhz speed. You can double it up to 16Gb, but games really don't use that, or spend money on faster ram, but the performance hike is going to be pretty small for the amount spent. Roughly $60 maximum right now.

As we are sticking to Nvidia, you are likely to have to pick between the GTX770 and GTX780. The GTX780 is obviously faster, but there is nearly a $200 price gap between them which at some point in the not too distant future will be filled by the GTX770Ti. By the time you purchase, it's possibly the GTX780 will be comfortably affordable, and the GTX770Ti will almost definitely be. An alternative solution might be two GTX760s, which would enable you to stagger purchase dates, but generally I'd stick with a single card. All three cards will eat through any game at 1080P, it really depends how much you have/want to spend.

Additional costs to consider are a CPU cooler and a new PSU.
New PSU is not essential but perhaps advisable, especially if yours is a few years old. A lot of PSUs are now being specifically labelled as Haswell compliant due to the unique characteristics of low power usage. Something like a 600W PSU is pretty comfortable for running any single graphics card but if you want to mess around with overclocking, a bit of headroom is always nice so I'd probably recommend around 650W for a single high end card and overclocked CPU. Seasonic is a great brand to stick with, but there are plenty of good, high quality options out there, Seasonic SSR650RM, Rosewill Capstone 650M, Corsair HX650, XFX P1-650X, to name a few.

For CPU coolers, that's a whole different conversation, but worth thinking about. If you aren't terribly interested in overclocking, but just want a nice return on investment, something like a Coolermaster Hyper 212 Evo is a nice improvement on the stock cooler for minimal outlay. If you fancy pushing the CPU further, things like the Noctua nh-d14 or Phanteks ph-tc14 are about as good as money can buy.