I did it for my brew space as well. I went with the big plastic tub style that can hold a sanke keg laying down. It has come in handy for so many things now, and I am very happy that I installed it.
I sweated the copper lines for both the hot and water cold lines and added valves there as well. For the drain, you definitely want to find a way to get it to be plumbed if at all possible. I brew in the garage/basement near the laundry, and we have a sump pump to pump the wastewater from the washing machine into the waste line which is near the ceiling of the garage/basement, so I just added a Tee there and so the sink just drains into the sump pump.
The costs will vary depending on the sink you want, and how much of the work you want to do yourself (if using copper, can you sweat copper and have a torch/solder/flux?), and where is your nearest drain pipe that you could tie into?
I personally would recommend not going with the bucket route, I can see that becoming a nuisance right away. When I clean my kegs, I soak them overnight completely filled with oxiclean, and then rinse them out, and I do two at a time typically - I can't imagine how many times I would need to pause to dump out a separate drain bucket.
edit - here is an old picture I found:
You can see the sink on the right side, and the sump pump right beside it. There are two copper pipes coming down along the wall on a 2x6, those are the hot and water lines that I Teed from the rest of the house. You can also see the last bit of the waste water line going to the septic tank, it is the large white PVC pipe going into the wall. I have only made minor modifications to the setup, it is essentially the same at this point, and has worked well for me!