spiral/helix cutting

I need to cut a spiral onto a silver rod.
The sides of the cut can be at 90 degrees/and/or inclined. I envisage this to be done by a lathe (milling machine?).
Diameter of rod could be 10-15mm, spacing between edge of the next groove ca 3mm, groove width & depth ca 2mm (ideally there should be some scope for visual considerations).
Non electric system would be acceptable (or very slow speed lathe), machine size should not be more than 1m, weight under 50kg. Cost should not be more than $1000-1500, but this assumes that it can be used for other applications, eg cutting tool steel etc.
I once owned a wood lathe (used it a couple of times only) & have used a larger metal lathe under supervision for spinning. Metal lathe users sites are so full of intalk that it is difficult for a novice to decipher the essential info. Any suggestions?
I thought of buying a sherline - but there must be cheaper options? A lathe (milling machine?) would be very useful as I would try to learn to use it for other work as well as I am a silversmith/jeweller.
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