Use cactus compost - easily bought in quite small bags. Cacti an succulents will root in pretty dry compost so don't worry abut keeping it moist. Are you sure it is aloe vera? the leaves look longer and thinner than mine. Ask Hywel what he thinks.

The roots look a bit sad, the roots on mine are poking out of the drain holes in the pots. However, it should do ok once it's in a pot.

The original Aloe Vera, from which I have had hundreds of offspring's from, I got from Tenerife. I dug a little plant out of soil that was so dry and hard it was like concrete. I forgot about it until I got home and planted it where it survived and grew well. So in my experience they are a very forgiving plant that will tolerate a lot of neglect.

Regarding what soil to use, I just use general purpose compost mixed with a bit of sharp sand. They always seem to do well and I get lots of baby Aloe every year to plant on and give away.