I just picked up this Asus 23 inch , 1080p, 2ms monitor and it I use it for the same needs as you and its a good monitor at a great price.
Right now Newegg has a 20$ off promo code with a 20$ rebate bringing the price down to 120$AR. At this price I would definitely pick one up.
http://www.newegg.com/Product/Produc...82E16824236175
I moved from a 1050p to a 1080p 120Hz monitor few years ago (on my GTX580).
120Hz is really good, and should be within your budget, try to get one.