Very unlikely your monitor is dragging down performance... as long as it can refresh at 60 Hz or better, you should be OK, I think. Might be something else; not uncommon with a new setup!

Go back and check everything else, like all the stuff Windows runs in the background all the time. etc. Another real helpful thing I learned was to do antialiasing through your video card's software, not the sim. Most cards are happier that way.
But if you're going to upgrade (and why not?), the best refresh freq is whatever your new monitor supports at the resolution you want to display. For FS like any other program, higher is good!!
For example: I have a nice NEC CRT that'll do 85Hz max. My graphics card will do that at 1024x768, so that's how I've got it set up. Looks great.
I normally have resolution at 1280x1024, but for FS it just works better at 1024x768 with my rig. For one thing, the user interface text is too small at 1280x1024...