buy a violin

I think you should buy 4/4size of violin ,
because I think your arm is not so short,
about how much ,
I know some violin is under $1000,
but some violin is above $1000
many difference types of price

maybe 3/4 is suitible for you .
About the cost, it depends on the quality of the violin.
Therefore, I can't tell you.
But, if you are the beginner,
no need to buy a expansive one.