Price. Price always comes first in my book. Value should come first but it rarely does. I go cheap most of the time. I do sacrifice quality at times but I can live with that. What is your budget for a flat screen monitor? Can you afford a slightly more expensive model?
Space. How much space will you have to work with? If you're like me, I still have a large monitor so space wasn't such a big requirement for me. Anything smaller than what I have is fine. I opted for the 22" monitor. Twenty two inches is way larger than I'll need but it's a comfortable size.
Quality. With so many models to choose from, it's difficult to know which one is the best. Staying with brand names such as Sony, Toshiba, Dell, or Samsung are safe bets. It's even better to look up that particular model online so that you can see the reviews of others who actually own the brand and model.
Your purchase of a brand new flat screen monitor should go smoothly if you follow those three criteria.