Well i don't intend on playing any FPS games like Call of Duty on it because i don't think my computer could play at 1920x1080. I may may may may may play games like SC2, however it will mainly be for a extension to my screen and especially for when i am doing programming.
Then one of the Ultrasharps will probably a good choice for you. From the resolution you mentioned im guessing you are looking at the 23". I understand that the 23" is within your budget. However, I really do recommend the 24" to keep the same 16:10 screen ratio as your MBP. And IMO 16:9 just looks too wide.
Also I think with the 24" you will need to get an adapter to dvi any bigger will need the dual link dvi. I think with the 23" you can use HDMI. My computer was before the mini display port and came with dual link DVI. So maybe some one else can help with that.