not really easy to build a "gaming" pc without a gpu... unless you're looking at a higher end APU. Intel integrated graphics sucks... even the low end apus eat the high end hd4000 alive. hd2500 is not capable of 3d graphics... you can play 2d games on them, but anything more complex then that and it will rapidly become unplayable.
If your budget was a hard 550, you probably would have been better off (and would have had a better gaming experience) going with a cheaper CPU/MB and spending the savings on a real GPU. that type of system would have worked much better.
For example, an AMD FX 6300 + 970 chipset MB + 7870 would have been a nice mid/high level gaming system and you could have managed it for 500-600. (barely)
Granted, later on down the road...
PCPartPicker part list /
Price breakdown by merchant /
Benchmarks
CPU: AMD FX-6300 3.5GHz 6-Core Processor ($119.99 @ Microcenter)
Motherboard: Asus M5A97 LE R2.0 ATX AM3+ Motherboard ($74.99 @ Newegg)
Memory: G.Skill Value 8GB (1 x 8GB) DDR3-1600 Memory ($29.98 @ Outlet PC)
Storage: Toshiba 500GB 3.5" 7200RPM Internal Hard Drive ($55.98 @ Outlet PC)
Video Card: PowerColor Radeon HD 7870 XT 2GB Video Card ($239.99 @ Newegg) ****
Case: Apex PCV-588 (Black) ATX Mid Tower Case ($39.99 @ Newegg)
Power Supply: Corsair Builder 430W 80 PLUS Bronze Certified ATX12V Power Supply ($26.99 @ Newegg)
Total: $587.91****
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-02-19 22:51 EST-0500)
****until the 22nd newegg is selling this card for $207... or $32 off; which would bring the total build to $555.91