What 120hz, 24 inch monitor should I get?

[Mubariz123]

[UK]
So im about to build my first pc, and it should be pushing past 60fps (on games like league of legends,) and i've been told I should get a 120hz monitor in order to reap the full benefits of going passed 60fps.

This is the PC i am going to be building:
PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i5-4460 3.2GHz Quad-Core Processor (£127.00 @ Aria PC)
Motherboard: ASRock Z97 PRO4 ATX LGA1150 Motherboard (£81.53 @ Ebuyer)
Memory: Corsair Vengeance 8GB (2 x 4GB) DDR3-1600 Memory (£59.98 @ Amazon UK)
Storage: Kingston SSDNow V300 Series 120GB 2.5" Solid State Drive (£43.99 @ Amazon UK)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive (£38.70 @ Aria PC)
Video Card: MSI GeForce GTX 770 2GB TWIN FROZR Video Card (£227.72 @ Scan.co.uk)
Case: Corsair 300R ATX Mid Tower Case (£59.15 @ Aria PC)
Power Supply: XFX 550W 80+ Bronze Certified ATX Power Supply (£44.11 @ CCL Computers)
Optical Drive: Lite-On iHAS124-14 DVD/CD Writer (£11.09 @ Aria PC)
Operating System: Microsoft Windows 7 Professional SP1 (OEM) (64-bit) (£44.99 @ Amazon UK)
Total: £738.26
Prices include shipping, taxes, and discounts when available

I already have 1 60hz 24inch monitor and I will be going with a dual monitor setup, would it hurt my eyes to keep switching between a 120hz monitor and a 60hz monitor?

Thanks for your help.

 

[theProbe]

I would change the GPU and MOBO. AMD offers much better price/performance ratio and you don't need a z board if you won't overclock.

 

[Mubariz123]

woops i posted the wrong build, I will be going with this MOBO (below), but I think im going to keep the graphics card, cus I would lke to use physx, do you think i would need a 120hz screen though?

http://uk.pcpartpicker.com/part/msi-motherboard-z97pcmate

 

[sora]

I would stick with two 60hz monitors or one 120hz monitor.