Best to date 850$ build

Solution
^yes if you can get the screen later or even not get it, you can bump your performance by alot and then save up for screen later

Cut out the cooler since i3 dosen't need it
Dropped to a cheaper motherboard with similar features (also one toms picked for the $600 and $800 system builders)
Cheaper ram and PSU
Stuck with the same case but there are cheaper ones that don't have USB3 and cheaper ones that do [subtract $10-15 for a cheaper case)
7850 2GB is actually the same price so get that instead since you going 1080p too

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: Intel Core i3-3220 3.3GHz Dual-Core Processor ($122.98 @ SuperBiiz)
Motherboard: ASRock Z75 Pro3...

tator_80

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Since your going with an I3, you don't need that after market CPU cooler. You only need one of those if you want to overclock. The stock fan will do you just fine.

Take the money you save from the CPU cooler and get an ASROCK Z77 Pro4

If your buying the monitor, but you already have one that would do, don't get it. Maybe even a 20" plasma tv would work. Save the money from that and invest in an I5 3570k.
If you do that, then consider an Aftermarket coolor. If your sticking with the I3 drop the aftermarket cpu cooler and grab the Pro4 motherboard
 
^yes if you can get the screen later or even not get it, you can bump your performance by alot and then save up for screen later

Cut out the cooler since i3 dosen't need it
Dropped to a cheaper motherboard with similar features (also one toms picked for the $600 and $800 system builders)
Cheaper ram and PSU
Stuck with the same case but there are cheaper ones that don't have USB3 and cheaper ones that do [subtract $10-15 for a cheaper case)
7850 2GB is actually the same price so get that instead since you going 1080p too

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: Intel Core i3-3220 3.3GHz Dual-Core Processor ($122.98 @ SuperBiiz)
Motherboard: ASRock Z75 Pro3 ATX LGA1155 Motherboard ($76.99 @ Amazon)
Memory: Patriot Viper 3 8GB (2 x 4GB) DDR3-1600 Memory ($44.99 @ Amazon)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($73.52 @ Amazon)
Video Card: MSI Radeon HD 7850 2GB Video Card ($169.99 @ Newegg)
Case: NZXT Source 210 Elite (White) ATX Mid Tower Case ($49.99 @ Amazon)
Power Supply: Corsair Builder 430W 80 PLUS Bronze Certified ATX12V Power Supply ($34.99 @ Newegg)
Optical Drive: Samsung SH-224BB DVD/CD Writer ($15.99 @ Newegg)
Operating System: Microsoft Windows 7 Home Premium SP1 (OEM) (64-bit) ($89.98 @ Outlet PC)
Monitor: Zalman MZ230ED 23.0" Monitor ($119.99 @ Newegg)
Total: $799.41
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-02-28 17:57 EST-0500)

CPU heavy build with i5

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: Intel Core i5-3350P 3.1GHz Quad-Core Processor ($180.98 @ Newegg)
Motherboard: ASRock Z75 Pro3 ATX LGA1155 Motherboard ($76.99 @ Amazon)
Memory: Patriot Viper 3 8GB (2 x 4GB) DDR3-1600 Memory ($44.99 @ Amazon)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($73.52 @ Amazon)
Video Card: MSI Radeon HD 7850 2GB Video Card ($169.99 @ Newegg)
Case: NZXT Source 210 Elite (White) ATX Mid Tower Case ($49.99 @ Amazon)
Power Supply: Corsair Builder 430W 80 PLUS Bronze Certified ATX12V Power Supply ($34.99 @ Newegg)
Optical Drive: Samsung SH-224BB DVD/CD Writer ($15.99 @ Newegg)
Operating System: Microsoft Windows 7 Home Premium SP1 (OEM) (64-bit) ($89.98 @ Outlet PC)
Monitor: Zalman MZ230ED 23.0" Monitor ($119.99 @ Newegg)
Total: $857.41
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-02-28 17:58 EST-0500)

GPU heavy build with 7870

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: Intel Core i3-3220 3.3GHz Dual-Core Processor ($122.98 @ SuperBiiz)
Motherboard: ASRock Z75 Pro3 ATX LGA1155 Motherboard ($76.99 @ Amazon)
Memory: Patriot Viper 3 8GB (2 x 4GB) DDR3-1600 Memory ($44.99 @ Amazon)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($73.52 @ Amazon)
Video Card: Diamond Radeon HD 7870 GHz Edition 2GB Video Card ($219.00 @ Newegg)
Case: NZXT Source 210 Elite (White) ATX Mid Tower Case ($49.99 @ Amazon)
Power Supply: Corsair Builder 430W 80 PLUS Bronze Certified ATX12V Power Supply ($34.99 @ Newegg)
Optical Drive: Samsung SH-224BB DVD/CD Writer ($15.99 @ Newegg)
Operating System: Microsoft Windows 7 Home Premium SP1 (OEM) (64-bit) ($89.98 @ Outlet PC)
Monitor: Zalman MZ230ED 23.0" Monitor ($119.99 @ Newegg)
Total: $848.42
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-02-28 17:56 EST-0500)

Screen less $810 build

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: Intel Core i5-3470 3.2GHz Quad-Core Processor ($188.79 @ Amazon)
Motherboard: ASRock Z75 Pro3 ATX LGA1155 Motherboard ($76.99 @ Amazon)
Memory: Patriot Viper 3 8GB (2 x 4GB) DDR3-1600 Memory ($44.99 @ Amazon)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($73.52 @ Amazon)
Video Card: Sapphire Radeon HD 7870 XT 2GB Video Card ($234.99 @ Newegg)
Case: NZXT Source 210 Elite (White) ATX Mid Tower Case ($49.99 @ Amazon)
Power Supply: Corsair Builder 430W 80 PLUS Bronze Certified ATX12V Power Supply ($34.99 @ Newegg)
Optical Drive: Samsung SH-224BB DVD/CD Writer ($15.99 @ Newegg)
Operating System: Microsoft Windows 7 Home Premium SP1 (OEM) (64-bit) ($89.98 @ Outlet PC)
Total: $810.23
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-02-28 18:01 EST-0500)
 
Solution

tator_80

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Jun 3, 2011
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Stickman went ham on the listed parts.. haha. Stickman's recommended Pro3 isn't much different from the Pro4, other than the Z75 vs Z77 chipset. Considering your going with the I3, Z75 is perfect.