You should strive to use strings that complement your bowed instrument or in other words, strings that balance the instrument’s sound. For example, if one has a violin with extremely soft tone, one should choose strings that give the instrument more brilliance (usually you can achieve that by using strings with higher tension).
In general, three sorts of strings are used on bowed string instruments. All three are known as wound strings, meaning that the core of one material (gut, metal or synthetic) is wound in metal (usually aluminum, silver, and chrome steel is used), except for violin’s E string which is usually made of solid steel.
Gut-core strings will give your instrument a soft tone with a lot of character, reminiscing the sound of the musicians from the beginning and the middle of the 20th century. However there is a downside to this: it takes 1-2 weeks of playing to stabilize the gut strings, and even than they will not last for long. They also tend to go out of tune faster when exposed to changes in temperature or humidity, making them more demanding for use outdoors, in churches etc. And last but not least they are the most expensive.
Strings for authentic baroque instruments are also made of gut, however they are wound differently and with other materials than modern varieties. Usually the upper two strings are bare gut.
Metal-core strings are the least expensive, last longest (about 1 year), but produce the least favorable tone. They also tend to be more sensitive to changes in temperature than synthetic-core strings and go out of tune quickly.
I can recommend only one brand of strings with metal core - D'addario. These are the only metal strings (that I know of) that have a somewhat similar tone to those with gut or synthetic core. You get a good tone for decent price, making them a great choice for beginners and amateur players.
On violin, it is common to use first string made of solid steel, or steel wound/coated with precious metals (e.g. gold, platinum).
Synthetic-core strings are most widely used strings as they are most practical and most responsive of the three. They don’t take long to stabilize, stay stable for a good period of time and are less sensitive to temperature and humidity changes.
There is a wide range of synthetic-core strings to choose from, so you should be able to find the best to complement your instrument. There are big differences in characteristics, quality and prices. Some, usually more expensive ones, produce somewhat similar tone to gut strings (e.g. Thomastik ?). But most of them do not produce as noble and as full tone as gut strings do.
All said, you might have to use a combination of different strings to balance the sound of your instrument on all four strings.
Interesting fact: In the middle of the 20th century it was popular to use soft two middle strings with gut core, and hard two external strings with a greater tension. It was believed that a violin with that combination of strings produces more brilliance on the outer two strings. Jascha Heifetz even used the middle two strings made of bare gut (not wound).