If you have no intention of ever playing any games other than sports games (NFL, baseball, golf only), or ever doing anything like graphics design/video rendering, will you get any benefit from having a dedicated video card?
Will you get any benefit out of an I5 or I7, instead of an I3?
If you don't use a video card, then your only choice is either crappy Intel HD3000/HD4000 graphics. They'd suffice for HD movies and playing games at low resolution (720p) and at very low settings. Won't be smooth though.
Core i7 does not benefit ANY sort of game, since most games actually suffer performance penalties from Hyperthreading (not optimised for it). Most PC games are GPU bound rather than CPU.
A Core i3 would be a good budget option for a casual gaming build,
A Core i5 would be best for heavy gamers.
Most sports games can already get by with a budget card like a Radeon 7770 or a Nvidia GTX650 (Ti). You will need to read the specification requirements on the game you intend to play.
($600) Intel Gaming/Multi-Purpose Config El Cheapo
CPU: Intel Core i3 3220 $117
Mobo: AsRock B75M-DGS $59
RAM: 8G Kit G.Skill-NT (2x4GB) DDR3-1600 $45
HDD: Seagate Barracuda 500GB (ST500DM002) $60
GPU: 1GB AMD Radeon HD7770 $112
Case&PSU: Thermaltake V4 Black Edition w/ USB3 and 500W Litepower PSU $75
ODD: DVD burner $19
Peripherals: [ 21.5" LG E2251T / Microsoft Wired Desktop 600 / Logitech LS11 2.0 ] (+$154)
Total: $641
Note prices are taken from MSY parts pdf. http://www.msy.com.au/Parts/PARTS.pdf