If I were you, I'd give up the idea of using something to convert it to an improvised wine rack, unless you have conveniently shaped decorative shapes lying around your house.
Otherwise, if you have the power tools and have some experience with woodworking, you can work on a Tower Style Wine Rack. It's a good project to take on, if you have the patience.
But since you live in an apartment, you likely won't be having power tools.
So my best advice to you would be to invest in a good wine rack (~$60- ~$150). The cheap ones will likely be just that, cheap (under the strain of more than 3 or 4 bottles, the joints will likely start to come apart).
I personally brought a wine cabinet from Wine Racks America
(google it if you'd like), and although it is a bit on the expensive side, the quality is superior.
For your intentions and purposes, I think the "VintageView 6 Bottle Le Rustique Wine Rack
" would be fine.