Neither the monitor nor graphics card would cause any graphical issues, if that's what you're wondering. If the monitor has the correct plug, the graphics card has the right plug, and you have the right cable, there should be no problems.
I have the exact same card, and I play Crysis 2 at 2048x1152 with ultra SMAA, and the high-res DirectX 11 pack, and I usually stay around 60FPS. So at 1366x768, you could expect to max everything out on every game you play.
You could get a new monitor (1920x1080) to really utilize your graphics card's clarity, and have more screen space. If you have the money. I use the SyncMaster 2343 and 2233 together, and both are great.
If you don't want to get a new monitor, I recommend setting your refresh rate to the highest possible. You can even "overclock" the monitor by testing custom refresh rates in the NVIDIA control panel.
After that, enable V-Sync in your games. High Refresh + V-Sync = Silky Smooth Gameplay!