@OP, no if you arent playing FPS games a 144Hz monitor would be an added expense.
Some will tell you to buy one no matter what, but for web browsing, email, browser games, RTS and the like, you wont even notice it.
Dont worry about Freesync and Gsync, if Freesync is on the monitor, it is ok, it wont hinder performance if you use a nVidia card, some manufacturers include it. However not needed unless you go over 60fps in games anyway and your video card will sustain high fps numbers. It does help with screen tearing in fast paced games however in WoW, vsync works fine as the input-lag on that engine is marginal at 1080p.
What video card do you have? I know its a nVidia card, but what model?
From what it sounds like, you just want a decent moitor, great colors that will get you by for a while.
Here ya go! and within your budget.
It has Freesync, but it doesnt matter in your case, and the speakers can be taken off the mount simply by puilling the tray out of the base and unplugging from the back.