I spent some time a few years ago teaching basic skills at a young offenders' centre. In one room there was a cage full of various instruments - guitars, drums, a couple of keyboards. They were never used because there was no-one able to use them. The lads often used to complain about not having access. Very sad. Guitar sounds like a good plan. You may even find a student who can play it. If you could learn a few popular songs then even better - you could plan something in for the first session and then ask your students what sort of music they'd like to play/sing. Try the 3- or 5-chord song books that are available - there's a very wide range of material in them.
My short experience tells me that inmates are generally responsive to any education. It gets them out of their cells for an hour or so and a little time away from having prison officers breathing down their necks. As one of them told me, 'you're not the one who locks us in at night'. That said, like any teaching, don't be too forgiving too soon - they'll take advantage. Also, be prepared to have any equipment, yours or the prison's, checked and scrutinised before and/or after every session. We used to be equipped with a kit box containing the requisite writing/drawing materials for the size of class, and it had to be checked out and in at every session. Once I was left with a protractor missing at the end of a lesson. I had to tell the officer on duty and all six lads in the class had to be strip-searched before they could go back to their cells and before I could leave the wing. It turned up behind a wall panel in the classroom three weeks later. The officers told me that the lads had probably just been testing me but every incident, however minor it may seem, has to be treated as an escape attempt. Very rewarding though, and a useful experience. Good luck.