Yeah, that'll work just fine with your hardware.

The only incompatibility the monitor would have with any of your hardware is likely the lack of a DVI input on your graphics card, but you'd still have a VGA input, so no problems there.

Your graphics card has a DVI input anyway.

For RPGs/adventures and such, that'll pose no problems. It wouldn't pose a problem for FPSs either.
And as for the native resolution, your monitor's would probably be 1680x1050p, but most games won't run at that. I've had a few problems with older games stretching a 1024x768p (or less, but non-widescreen) picture over my laptop widescreen which has a native resolution of 1280x800p; the picture looks like someone sat on it and squashed it vertically, so be aware of that. Newer games have support for most resolutions though.