Wow, that's one that will get you loads of responses with differing opinions. It all comes down to personal taste, but here's my .02...
When I make anything out of wood, I prefer a strong grain pattern that will be highlighted when I either stain or stain & seal. I have used red oak & white oak (the white oak is more dimensionally stable which means that as you cut it down to size, it is less prone to warping & cupping) The oak family is also relatively cheap if you get it at a lumber mill or local lumber supplier. Anything you get from a chain store (Lowes, Home Depot, Builders Square, etc.) will already be planed & cut to size (read more expensive). If you don't have the equipment to finish a rough cut of wood, most lumber suppliers will do that for a nominal fee which still comes out cheaper than the chains. You can also step up to some of the more expensive woods (Cherry, curly maple, walnut or some of the exotics teak, brazilian koa, etc) but you are talking logarithmic leaps in price. You can also make use of other materials by adding metal sculpture to a wood frame and this would be rairly easy to make a jig for bending the metal into the shape to support the bottlesand mount it into a 3 piece frame for support. The advantage there is that there is less wood working to make everything symmetrical, you can paint the metal to match any decor and it would be faster to fashion your rack. You could even go to a glass maker and have them fashion scalloped glass pieces our of thick stock and use that as the bottle support...?
Boy, I guess I gave you more than .02 worth but you should let your imagination run wild.
Like the title says, use whatever looks good. If you have a roommate/spouse that is going to be looking at this every day and wondering what they got themselves into by allowing the hobby, then it better look good, or you'll be paying for it later. If you're lucky and you get some leeway, then you can go cheap and promise to upgrade later. Fortunately, I'm part of that lucky second group, so I bought two years of "later" after the first "cheap" rack.
This is my latest rack:
Each cubbyhole holds twelve 750mL bottles or about eighteen 375mL bottles, so I have room for 29 cases of wine(or the results of about 14-18 kits, depending kit yield). The construction is kinda cheating. I used "cheap" plywood for the carcass, with poplar horizontal shelf supports, with a solid cherry faceframe, with a cherry veneer on the sides. I painted the interior sections, and did a stain and polyuerathane finish for the exterior. The next step is to put doors on the cabinet to cover the wine and mini-fridge. Those will be cherry rail-and-stile doors, with a plywood floating panel.
White oak and mahogany are the best unless you want to go with a metal that will not rust like Stainless steel. You dont want Iron in there as a wine cellar is typically around 65% humidity. Both of the woods I listed were and still are used in boat building and can withstand wetter climates. White oak has a much better tensile strength and is what I built mine from. Would love to post some pics but dont know how to on this forum.