i don't think purchasing a bigger monitor would help for web browsing, although if your HDTV is 24in+ and 720P i'd recommend getting a 1080P monitor atleast 23in wide. big 720P TVs look really bad because of the size/pixel ratio. a 23in 1080P monitor would look great for gaming.
to sum it all up, no. do not get a better monitor just for web browsing.