Monitor for A Laptop

I have a Lenovo Y580 and the screen size is getting to me. Now, before you start typing wildly at your keyboard asking me why I didn't just build a desktop and a monitor, let me explain: I am a student currently living in the US, but I am returning to my home country in the summer. I needed a laptop for school, but gaming as well. I want to be able to take advantage of the mobility of the laptop, but also have a nice, big screen at home when I am there, so that I can game and code with a larger viewing surface. I have a desktop at home, but it is two years old, and my laptop is faster.
So, does anyone have any suggestions or experience with using a monitor with laptop?
I don't think there should be any issues with compatibility or whatever, but let me know if anyone has any problems.

Requirements:

Size: 22" to 24"
Price: From $100 to $175, preferably.
Approximate Specs: 1920x1080 is required. 5ms speed is fine, since 2ms is seeming to be expensive where I have looked. Preferably Full-HD. LCD or LED, either is fine. HDMI port is a must.

Thanks!

well, you described pretty much every single TN panel monitor in that size. get an asus off of newegg, and have it shipped to the university. I suggest you bring it back and forth if you can, I really find it useful to have an external monitor for school.