Beginner Gardening: Should I Transplant This Succulent?, 1 by Chillybean

Chillybean wrote:
I bought it at Lowe's back in April, but don't remember its name. They were sold along side the cactus plants. There has been some new growth, in spite of my usual black thumb. I don't need to water it often and it sits in a room with a south facing window.

I am pretty pathetic with any plant, but if my normal care doesn't kill it a transplanting usually does it in. If I need to transplant can you walk me through this a little? What would be the best type of soil, and does it need to be a deep pot, or maybe more of a shallow but wider one?

It does seem to be attracting fruit flies, is there a remedy for this? We have cups of vinegar and soap nearby to help with that, but there are still some around. I spray it occasionally with an insecticidal soap, but don't want to overdo it. I have a hanging plant of some variety, but I haven't seen any fruit flies congregating around that.

Thank you so much for your help.