Maddie, I'm not good at identification but have to agree with you that it looks like an echeveria. It's a nice looking plant and Seems to have a bloom coming.

Succulents are specialized plants which hold water in their leaves and stems, so they prefer dry conditions and should never be overwatered or even sprayed with water. They can easily rot if too wet. Your pretty plant should be repotted in fast draining cactus and succulent soil in a small pot with drainage hole in the bottom. (Growers don't use the best soil for succulents and they almost always need repotting unless you buy from a special succulent nursery.) You can sit the pot in that basket if you want, but plants generally do better if they aren't double potted. Don't know your gardening zone, but your plant should be slowly transitioned into full sun. Water only when you are sure it's very dry. It's such a healthy, pretty plant. Please take care of it and you will be able to enjoy it for years ahead.