My guess at the ID would be Pachyveria glauca.

The first thing I would recommend is to buy a bag of perlite and mix it with your soil about 60% perlite or more - this will be critical in aiding drainage in that moisture retentive soil. Also, don't let the plant sit on that saucer after you water it, make sure it's drained well before putting it on the saucer to avoid the pot sitting in / wicking up more moisture.

The pot may also be a bit too large for the plant, kind of hard to tell for sure in the photo.

It will need sun. How much depends on your climate, acclimate it slowly to more sun until it gets a few hours or so a day.

Good luck, let us know how it goes!

Your succulent looks like some sort of pachyveria or pachyphytum. It will survive indoors, as long as you give it as much light as possible and water sparingly. Your soil looks water-retentive, and you should generally avoid that when owning succulents. I would recommend mixing the current soil in a 50/50 ratio with perlite or pumice. Succulent leaves will occasionally wrinkle and dry up as they age. Other times, they will become yellow and mushy when overwatered and dry and crispy when underwatered.