When you purchase a new violin, it should come fully setup, professionally adjusted, and ready to play. It should be inspected for, among other things . . .
- The height, curve, fit, placement, graduation, and tuning of the bridge
- String height and spacing at both bridge and nut
- Proper cutting of nut grooves, wide enough for the chosen strings, with no sharp edges or angles
- Tail-gut length and after-length tuning
- Fitting and lubrication of pegs
- Proper installation and lubrication of fine tuner(s)
- And, the condition and proper installation of the strings.
- Strings should be selected to match the character of the instrument
- And, the bridge and soundpost should be adjusted for optimal tone and response.
This attention to detail and skilled adjustment of a violin is arguably more important than the quality of the instrument itself. A fine violin, poorly adjusted, will sound and play poorly. On the other hand, a mediocre instrument, if properly adjusted, can be perfectly suitable for an beginner or even advancing player.
Of course, the best scenario is to get a fine instrument that is properly adjusted. But, if your budget prevents this, or if you have an old violin from Grandma that you're hoping to use, then I impolore you to take it to a qualified luthier for a workover, before trying to learn to play on it. Tell her or him that you'd like it fully adjusted, including all of the items above. Now, depending on the condition of the violin, this may not be cheap. New strings alone can run over $100, fitting a new bridge $75 or so, replacement nut $25-$75, and overall tonal adjustment another $50-$100, just to name a few of the more commonly needed items. (Which is why it's often a better idea to rent a quality instrument, when you're getting started.) But, if your violin is in decent shape, this could be the good option.
Also, keep all of the above in mind when considering the purchase of a cheap violin on the internet. Factory instruments selling for $50-$100 are what teachers frequently refer to as VSO's, or violin-shaped-objects. They may look like violins, with the right shape, four strings, and a fingerboard. But, they are not typically adjusted well, the strings won't be set correctly, and frequently they are so cheap that they can't even be adjusted.