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Once you get a bit more experienced and feel like sticking for it for a few years, you'll want to look at the wood, the shape, the sound/timbre/tone of the actual instrument, which means going into a shop and trying all of them out and possibly renting them for a week to see how they feel. And you'll want to get better strings (mix and match different brands, some brands produce very bright sounds that work well for A & E, but I prefer deeper Ds and Gs, for instance) and a decent bow, which can easily go into the hundreds depending (you'll want to try out balance and weight for bows, lots of people have multiple bows they use depending on whether they want a heavier or lighter sound). Very, very generally, the older the instrument, the better; older instruments tend to have better sound quality, and in the hands of a professional, they sound absolutely heavenly. Even if you only plan to play as a hobby, if you want to play for a longish time, I'd say it'd be a good idea to get a violin upwards of at least $1000. $2000 is when you start getting pretty decent instruments.
Also, if you want to go even a little serious, consider getting a private teacher. Don't get a private teacher for the basics, ofc -- you can teach yourself that -- but once you get to the slightly-less-shitty stage, you'll want to start refining your technique, and the difference between trained and non-trained musicians is like the difference between night and day.