I also read somewhere the CO2 is UV and invisible, which is a bonus.
CO2 lasers are far infrared, totally invisible except for the thing that's now on fire.
Not really a bonus at all, unless your goal is to secretly set things on fire.
They are very good at cutting/burning things though, most things absorb infrared instead of reflect it.
eg, stuff like clear plastic which a visible laser would just pass through or reflect off appears totally black to an CO2 beam so it heats up and melts nicely with little loss.
CO2 lasers are also relatively simple and easy to scale up for high power, eg 100W
Disadvantages are, as you say, not portable or easy to use. They need gas and water cooling.
For playing with, lasers a diode laser is far more interesting. A 8x DVD diode or blue laser projector diode will burn things if focused but wont cut anything except very thin items, eg 1mm thick.
They will of course permanently give you eye damage if you get a direct strike, especially the laser projector diodes as they are usually 1-2W where as a DVD burner diode is usually around 300mW
Just for the "cool" factor i recommend an Argon Ion laser.
It wont burn anything but looks cool and is semi portable. Here's my one.
1000W input about 25mW laser output, thats argon ion for you
Be careful getting into lasers, they have a tendency to multiply until you have too many.
Check out the last pic.