People usually buy violins, but in some circumstances it is possible to rent an instrument instead. We generally find violin rental to be useful in situations such as:
Outside of these situations, it's usual to buy a violin, which we usually do recommend, as it allows you to develop a 'long term relationship' with your instrument. (Also, many violin shops only rent out child-sized instruments, and not full sized instruments. This is usually to encourage people to buy full size instruments outright.)
If you buy from a shop that specialises in string instruments, then it's worth asking about part exchange before you make your initial purchase. This is a service whereby the violin shop will take back the instrument that they originally sold to you, and count some of the value towards the purchase of another instrument. This allows you to upgrade to a better quality instrument when you need to do so.