This looks to be a Crassula perforata also known by the common name "String of Buttons". The main thing to remember with growing most succulent is that they don't like soggy soil and they need very bright light.

First the soggy soil issue. There are many discussion on the forums here about soil and in particular gritty mix. This can be overwhelming so in the mean time before you purchase more plants, as I'm sure you will (they are addicting after all), Id start with mixing Perlite with a standard garden soil. Just be sure the at least 50% of the final mixture is perlite so it will drain quickly when watered and air can circulate better.

Pot choice can also play a huge role in soil moisture retention. Most important is to always have drainage holes. Terra cotta is by far the best choice for succulents since it also allows for circulation. For example, if I water my plants all on the same day, the plants in terra cotta will be dried out within 3 to 4 days while the plants that haven't been replanted from the generic plastic pots will stay wet for a week or more depending on temperatures and pot size.

Finally place it in a bright spot. If you're plant can't be outside then a south window will usually get enough light to keep it from stretching out.

Those plastic sleeves are great for transporting plants, but terrible for growing them. Take that off right away and allow some air circulation for your plant.

The spots on the leaves may be normal. (I can't see them well enough.) Do they look like the ones on my variegated form of this plant?

I agree with Nicholas on repotting and light.

When you see a plant with longer than normal spacing between the leaves, it may be because it is not getting enough light. Notice how much closer together the leaves are in Crenda's photo. You plant will be happier outdoors as long as it is not too cold. Filtered outdoor light, a slightly larger pot with a hole or holes in the bottom, and cactus mix will help it grow.