The subject of shoulder rests has generated a lot of controversy amoung teachers and violinists. Because they were not used until fairly recently and also because they may affect the sound somewhat, there are still some teachers who recommend against using them at all. Certainly, there are some violinists who do fine without a shoulder rest. Often, these people have short necks.
For example, David Oistrakh, one of my favorite recording artists, fits this mold!
For the rest of us, a shoulder rest can make playing the violin much more comfortable. It frees the left hand from having to support the instrument and should allow the violinist to play without raising the left shoulder. The choice of shoulder rest depends on the unique physiology of each student. Sponges (even a kitchen sponge with a rubber band) and Play-on-Air are examples of padded rests.
There are also various rigid models with feet that are produced by many manufacturers. Each fits slightly differently.
In sum, my recommendation for selecting a shoulder rest is to try several and look for a comfortable fit. In the case of the rigid models with feet, the pad should rest securely against your shoulder and collar bone without any gaps between you and the rest. Try to find a violin shop that has a selection of rests and will allow you to try them. Adiditionally, your teacher should be able to help you assess fit.