You will most definitely see a difference. Trust me. Go for one that does HD quality, but keep in mind those other features help as well, like for example the contrast ratio or if it has say, IPS technology. Take a look at my monitor:
http://www.amazon.com/gp/product/B008RM235I/ref=oh_details_o07_s00_i00?ie=UTF8&psc=1
It has the basics, an excellent quality screen, and built in speakers. Features such as contrast ratio are usually 10Mil to 1, this is 30 mil to 1. All that, and it is $159. Not bad IMO.
Shop around of course, but to answer your question simply, there is a huge difference going to a larger resolution monitor, especially for gaming.