I don't think affordable and ornamental turning should be used in the same sentence. I know that a good cross slide will be in the range of $100 plus. The additional tool post needed will be expensive unless you have a milling machine and metal lathe.
A Dremel tool on an auxiliary tool post and a X Y table is feasible, but still not reasonable in cost. The Dremel and X Y table will be about $150 plus the cost of the tool post will run it over $300. You will also need an indexing wheel, homemade is reasonable, to buy one is expensive, the best I have seen runs about $200.
My costs so far on what I have played with is well over $200, and at this point I have a used X Y table, a Dremel. a homemade indexing wheel, a pile of scrap metal and some wood that has been "ornamentalized" beyond recognition. That is using my my metal lathe and homemade mill.
Can it be done? Yes and no, just takes time and more time and not minding that you are throwing away money when you fail and start over. Will I ever be happy with my results? Probably not, I will probably try to improve perfection to see if I made mistake somewhere the first time.
Marvin