Got to Best Buy or Fry's or Sam's or Costco and look at some. When you find one you like then go online and research prices. I've been extremely satisfied with cheap brands such as I-INC and such and found them to be as good as name brands. A 19" under $300 is very doable including name brands. Newegg, Tigerdirect and others are mentioned a lot in these forums. Also look at Tom's hardware for comparisons.
For your needs refresh rate and resolution are key factors.
Im a gamer with a 256 mb nVidia card. I am looking at buying a new LCD to play my games on (F.E.A.R. and Oblivion) and im not sure what i should be looking for. My budget is about $300 and im thinking about a 19' widescreen but not sure what brand.