Another Vote for DIY
The plumbing will be the most expensive part no matter what. To run water to my darkroom, which is in my garage, cost over $3000. Ridiculous.
The sheet rock is cheap and I bought cabinets at the local Lowes. Then I used 3/4" plywood for the counter top. Cheap.
Never let plumbing scare you. It has always amazed me how much people have paid for what is relatively simple plumbing. Living in the country where I do, has forced me to become very resourceful, with pumps to maintain, and a local shortage of plumbers.
As long as you are quite comfortable with the use of a propane torch and copper pipe, you will have no problem with running in hot and cold water.
These can be teed off existing hot and cold water lines. First, locate a nearby hot and cold water pipe. Dry fit the run to where you want the new sink to be. Then disassemble the run, and using sandpaper, clean the ends of each run of pipe and the inside of each fitting till it shines. Apply acid core flux to the ends of each fitting (tees, elbows, unions, etc. and to the runs of pipe itself. Pay particular attention to the pipes you tee into for the water. You need to completely drain all water from that pipe and clean it meticulously, otherwise you will have difficulty heating it enough to get a reliable joint.
Make sure you install shut-offs on the new run so you can isolate the run in case of leaks. These can be installed at the end of the new run, but perhaps are better installed where you tee of the existing pipe, as the complete run may be isolated. Of course, you can also install shut-offs below the new sink and at the beginning of the new run. This is the best option.
Then work your way back to the destination, heating each joint, then applying solder and contiinue heating until it sweats into the fitting. Sweating is when the solder flows back into the fitting - the point where you can consider the connection good. Wipe the connection with a rag immediately after soldering to remove excess solder and flux. This will prevent future corrosion at the joint.
Drain plumbing can be a bit more difficult, especially in the situation you are in. Options include: (a) Running the drain to an existing grey water pump or a sump pit. (b) Installing a new grey water pump and reservoir such as a Sanishower (see link below), and then up to an existing waste water drain. These can be purchased for 2-3 hundred dollars. There are a number of brands available - some are intended for basement bathroom installation, and include a small tank and pump using a float system to pump water up to the drains when a preset level of water exists in the tank. ABS drain plumbing isn't difficult. Again, it is a matter of dry fitting your run, ensuring that each run has a slight angle downwards so that water doesn't remain in the pipe, then cleaning the cut ends and fittings, then using abs cement on each pipe end and fitting. Locate your pump close to the drain, and you won't need to vent the run.
I do recommend aganst running your drain into a regular basement floor drain. Depending upon your areas plumbing codes, these may go to a municipal waste drain, but often only tie into your weeping tile, and/or storm drain only, which would leach trace chemicals in the drain water into the soil surrounding your house. In most jurisdictions, this would be illegal.
Hardware stores such as Lowes, Home Hardware, Home Depot and others can be an excellent source for not only items needed for your installation and for advice not only for what you need, but also for how to do it. There are also a number of internet sites which deal with plumbing basics.
Don't let plumbing intimidate you! Things should go better than you expect, and the experience will leave you better prepared for the next plumbing emergency, especially if it occurs on a weekend or holiday.
One resource of many you will find on the Internet is:
http://www.diyplumbingguide.com/
A good source of grey water pumps is:
http://www.saniflo.ca/?gclid=CP2hq4nZ-JICFRFBFQodtkqUGw
Dave