A guitar is nice but bulky. It can also easily break.
The jaw harp is a very simple instrument that you play with your mouth and your hand. You can buy them in many musical instruments shops across the globe, for about 5 euro. It's usually made from metal.
A quite easy to learn instrument that doesn't use up much space. Often called a harp, though that is actually a different instrument. There are mainly two different kinds of harmonicas, chromatic and diatonic. Diatonic harmonicas are more common, a bit smaller and often quite a bit cheaper. A free page where you can get tabs is from harptabs.com.
The basic idea is to breath in and out of the holes, sometimes in chords and other times in single notes. When you get used to this it's possible to get more notes out of the harmonica by bending, that means to regulate the air flow in your mouth. In the holes 1 to 6 you can do this on the draw (inhaling) and blowing in the holes 7 to 10. One way to try and learn this is to put your mouth on lets say the 4th hole (only!), put your tongue almost by your upper front teeth, draw in through that hole and slowly pull your tongue backwards along the palate.
- 3 = three blow
- -3 = three draw
- -3' = three draw bent a half step
- -3´´ = three draw bent a whole step