The core of the strings will affect the sound. Most often, you will find steel, synthetic, and gut cores. Gut cores are the original types of violin strings, going back several centuries. They are made from the lining of sheep intestines and offer the lowest tension. These are much more maneuverable with your fingers, allowing for more finesse, especially when playing classical music.
Generally speaking, steel strings offer a quick response and a clear, focused tone. However, you shouldn't expect a lot of depth or complexity from these. Also, ask any acoustic guitar player you know and they'll tell you; steel core strings are rough on the fingers, especially during long practice sessions.
Synthetic core strings use a strong type of nylon, similar to other string instruments, which are just as flexible as gut core with a much more stable pitch. While they don't sound just like classic gut core strings, they do produce incredible tonal sounds of their own.
All in all, there is no right answer when it comes to choosing a core. You just have to pick what's right for the style of music you enjoy playing.If you have multiple violins, you can use different strings for different music, but that's up to you!