That's a tough budget unless you do used. A low end but new monitor (I'm using one right now) will run you around $120. Mine's an LG that's 1080p and 22 inches. Keep in mind that last time you got a computer, screens were likely not widescreen. Because they're measured corner to corner, a new 22 inch monitor is about comparable to an old school 17-19 inch monitor.
So you really have around 380 to play with... for your computer.
With that budget I'd drop the video card requirement and go with integrated video with your cpu (it's free).
I'm sure someone here will help you with a build but also check out
https://www.reddit.com/r/buildapc
There's a lot of good resources there.