Monitors come in a very wide range of sizes, from small 15 inch screens up to massive 30 inch screens. You should pick a size that fits your desk area, but also your budget. Larger monitors are naturally more expensive, but the prices on most 19-24 inch monitors are under $300 these days. The most common computer monitor sizes today are in the 19-22 inch range. This size is good for most any task, whether it's web browsing or playing games.
You'll also want to determine whether you want a widescreen or standard monitor. Widescreen monitors usually have a 16:10 or 16:9 aspect ratio, while standard monitors have a 4:3 or 5:4 aspect ratio. That means that standard monitors are more square shaped, and widescreen monitors are more rectangular. Widescreen monitors are good for work and browsing the internet, as you can have multiple windows open side-by-side.