If you weren't planning on overclocking an i5-3470 would be fine.($200)
ASRock Z75 Pro3 for motherboard.($85)
CORSAIR XMS3 8GB (2 x 4GB) 240-Pin DDR3 SDRAM DDR3 1600.($62)
Zotac GTX 650 Ti BOOST.($170)
ENERMAX NAXN ENP450AST.($45)
You probably will never need a disc drive but if you do they're like $20
$218 leftover for a case and hardrive(Maybe even an ssd). If you are planning on playing any other games, get a better video card(like a 660 ti or 7870). Even the system listed above is probably overkill for LoL. Newegg has an excellent guide on how to build a computer:
http://www.youtube.com/watch?v=lPIXAtNGGCw . It's actually not hard at all, it's like Legos for adults.