Don't bother getting a new monitor that's only 1366x768.. That's not even an upgrade! 1280x1024 at 17" is about 96 PPI (pixels per inch) while 1366x768 at 18.5" is about 84 PPI.. You can get a good 23" 1080p monitor for like $150 at newegg.. 1920x1080 at 23" is still about 95 PPI.
Asus 23" 1080p Monitor (159.99@newegg)
That monitor is $20 off until January 14th, plus you can get a $15 rebate, so you would end up only paying $125!
I can't really answer your question about whether or not your PC will run new games, I don't have any experience with that exact build, and it's not easy to find benchmarks of old CPUs with new games.. If I had to guess, I would say it probably won't run new games with all the settings turned up, but probably would be ok for medium settings, and still look good! The best way to find out is to see for yourself when those games come out!