For my 2 cts, building is cheaper, buying is easier. If you make something that you want to show people into, then it can be expensive. I never really understood that thinking however and never particularly cared to show off a collection of anything. The cellar was for storage prior to drinking, that's all.
In any event, you can build something fairly quickly. Then you need to figure out how you'll cool it. You can pay a lot of money for wine cooling devices or trick out an air conditioner. The cooling principle is exactly the same in both cases, they're just sized for different purposes but if you get an oversize AC, and the smallest one you can buy is going to be oversize, you'll have sufficient capacity to drive down the cooling temp w/out too much problem. In your area they use old ACs to build meat lockers, which need to be colder than a wine room.
Racking, as mentioned, can be expensive. If you're handy, you can build them yourself. If you buy them, they'll cost you more.
Racking is going to be the issue no matter what you do because there's not a perfect solution. The best is probably to have a separate slot for each bottle. That also wastes the most space so over-build if that's the direction you go.
If you buy a wine fridge, you can never really find the stuff in back unless you take out everything in front. If you make bins, it's a real pain to take out the bottom bottles, particularly if you have Rhone-shaped bottles, which don't stack very well at all. One thing you could do however, is make the racks slightly angled so that when stacking, the wine won't want to dump on the floor.
Also, if you build, make sure you learn all about insulation and where you put it. It won't do you any good to insulate the hell out of your walls and ignore the ceiling and door. Whatever has the least insulation is what your cellar will have. I can't stand fiberglass, but when people build cellars they always insist on using wood studs and fiberglass insulation for some reason.
Finally, if you're in a place where you may get basement floods, think about that. If you use wood racks, which you probably will, I'd put a coat or two of polyurethane on them first. Easier to wipe off spills too.
There are some other threads on this subject, both here and on other sites. Do a couple searches. Good luck.