Step 1: Where to buy
But even if your teacher instructs you, you will need to find a cheerful music shop that you trust. You are NOT looking for a shop full of electric guitars here: they need to have at least some expertise with stringed instruments. They needn't be slap next door, but you should be able to reach them relatively easily.
You are going to need strings, sheet music, stands, repairs (or at least setup), bow rehairs, and so forth. OK, you won't need these things every week, but this will be an ongoing relationship. So find a suitable retailer and get to know them.
Then go there, tell them how much you want to spend, and ask their advice. They know that if they make you happy, you'll be back for all the things I listed above - and in a few years, a better violin. And a few years later an even better one. And a new bow. And....
It's in their interest to satisfy you, and they know more about what student instruments are available than you or I ever will.