That looks like an Aeonium, or a Sempervivum. I am leaning toward the latter, but I can't be sure, since it is so small. I believe they do the best outside. Also, make sure the pot has a drainage hole, otherwise you may run into some trouble. Make sure you don't overwater. A good mix of soil to use would be 60% perlite, and 40% cactus and succulent soil. That should at least keep it from rotting. If you choose to put it outside, expose it to sun slowly. It may burn otherwise. I hope I helped! ~palmsandsnow

It doesn't need much bigger pot. If you repot, get only next size up, and use well draining mix. Little more potting media wouldn't hurt - it is better for the plant, and it will look much nicer if higher up in the container (it is sitting too much inside now) - JMHO.

Spot on Breton! Pronounced exactly the same as Jill/Jillian and according to my avatar, I appear to be female:-) As far as the plant is concerned, I'm guessing that Hobbits come in different shapes and sizes, just like we do! Maybe when it's grown a bit more and settled down it will show its true colours, it looks healthy but immature at the moment. It's got some good folded leaves already. Gill/Gillian

Save for the one in the 2 brown boxes in the second picture, you have troplcal succulents called echeveria(first image, second image front one) and sedum hybrid(yellow looking one). These plants are related, they are not cold hardy, like gritty coarse soil, best kept indoor during the winter. The other one(2brown boxes, left in the second) is a semperivivum, a hardy alpine succulent from europe, and must be kept outside during the winter(it needs a cold rest). Water them weekly in summer, and twice/once monthly in the winter, water sparsely just enough to moisten the soil.