Determine your price range before you start shopping! Yikes, violins range from sub-$100 to millions of dollars. I can tell you from testing various violins from $400-$1,500, I loved the Viviano Vitale over anything else in the sub-$1,000 range. However, that is for my taste, my wife preferred the sound of a different make. Since the violin was for me, I purchased the Vitale. If my price range were higher, I’d probably have ended up with the Tia Bruna.
If you have a violin shop in town, try out several in your price range and see what sounds good to you. Each of us has a different preference and each violin will sound a little different, even from others of the same model. Find a bow that gives you a good sound and try to use the same bow over multiple violins. At one point, I borrowed a $300 bow from a violin shop and thought a violin sounded great, but then I played my own, rented violin with that bow and it also sounded better than it normally did.
I’m fortunate as I have three violin shops within a half hour drive of home. However, after trying over a dozen violins and finding that I only really liked those above my price point, I ordered from three shops and did comparisons on those. Two were very good, one, not as much. The Vitale is the one I really liked in my price range, but you may find you like another model or have a different price range.
There are video demonstrations of a number of brands and models on youtube.com. Listen and compare to give you a general idea of what a violin sounds like, but it will sound different when you’re playing it.
Good luck and don’t rush! Take the time to find out what you like and find a violin that you will love.