Unless you will really, really be strapped for room where you're moving, there wouldn't be a big difference between a 22" and a 24" monitor. Sure, the 22" is smaller but either way it fits under your arm and you can lift it with one hand if you don't have any disabilities.
I have a 27" monitor that can easily fit under my arm and be carried with 1 hand.
This is the monitor http://www.lg.com/us/commercial/lcd-computer-monitors/lg-24EN33VW-B it comes with the power and d-sub cables. I don't need to buy a separate HDMI cable or anything to get it connected to the PC right? Yea super noob here lol.