1) Many games will fall below 60FPS with the quality settings on maximum even with the GTX780.
2) 120FPS is very hard to hit with modern games. VSYNC will just punt you back down to 60FPS if you can't achieve over 120FPS anyway, and you don't want VSYNC OFF or you get screen tearing.
3) 60FPS is still pretty smooth in most games.
4) It's much better to get a QUALITY 60Hz screen then a "cheap" 120Hz screen. There's a lot more to a screen than just the refresh rate.
As mentioned, a monitor with this feature is the PERFECT solution for you, aside from the price. I didn't bring it up because you said "cheap" 120Hz monitor and the first one is likely over $400 USD (whatever that is in POUNDS). Basically, at least 80% of your GTX780 cost likely.
5) *so the "best monitor" depends totally on your BUDGET. It goes something like THIS:
LOW BUDGET - best 60Hz monitor
MEDIUM BUDGET - best 120Hz monitor
HIGH BUDGET - 120Hz G-SYNC monitor (Asus has first dibs; likely Q1 2014)
HIGH BUDGET alternative - 27", 2560x1440, 60Hz, but NOT a G-Sync (higher resolution, larger screen but lacks G-Sync benefits)
HIGHEST BUDGET - G-Sync AND a 27", 2560x1440 screen (probably "only" 60Hz but G-Sync reduces the lag issues so much that gaming above 60Hz isn't really needed aside from 3D).