OCing i5-3570K, need a $30-$70 cooler

Hi, I am planning on building a desktop for Gaming, here is the basic specs:

Processor Intel Core i5-3570K 3.4GHz $229.99
Motherboard Asus P8Z77-V LK $144.99
Memory Corsair Vengeance 8GB (2 x 4GB) DDR3-1600 $53.99
Graphics EVGA GeForce GTX 670 FTW $407.99
Storage Corsair Force Series 3 240GB $179.99
LITE-ON DVD Burner - Bulk Black SATA Model $17.99
Enclosure NTZX Phantom 410 $100.00
Power supply Corsair HX650W $114.99
CPUFan COOLER MASTER Hyper 212 EVO $29.99
Total: $1279.92

I plan doing only minor OCing (say 3.7 GHz) at the start but eventually I might want to OC moderately(say up to 4-4.2 GHZ) and I am planning to get a Cooler in the $30-$70 range that can keep my Ivy Bridge CPU at a safe temperature during OCing. My first choice was Hyper 212 EVO b/c the price but I also looked up Thermalright True Spirit(140mm- $40), Thermaltake's Frio($60) and Corsair H60($65).

My question is for what I need(moderate OCing) which fan is the best and which one have the best value(price/performance), If I can get better cooling from a nosier cooler I am OK with it as long as it is not obnoxiously loud.

p.s If you have experience playing BF3 while OCing please let me know what setting you are on, how much did you OC and how much did it help your FPS, I am going to be playing BF3 a lot on this rig so I could use that information.