That tubing is just plain old vinyl tubing available at most hardware stores. Generally it is sold by an inside diameter followed by an outside diameter, for example 3/8"I.D.x1/2" O.D. You can just take a piece of it along to the hardware store with you. In my experience, Home Depot vinyl tubing is pretty cheap, I got my last batch at Ace Hardware, which seemed to be slightly higher quality. If you want really high end stuff you can go to tygon tubing, which is chemically inert, used for sensitive food operations or gases. The stuff is about a buck a foot, but does not kink. Probably overkill for a Westy. The standard vinyl tubing should be fine. I would suggest buying a hose barb fitting, connecting the old vinyl hose with a new vinyl hose and simply pulling it through the back of the cabinetry. You can buy either plastic or brass barbs, either one will work in this case. Sorry I don't know the exact length or diameter, but it's not very expensive stuff. I would allow a an extra three or 4 feet just to be on the safe side. I would think you should be able to guesstimate what it would take from the water tank to the sink. 10 feet sounds about right, maybe 12 to be on the safe side. Stainless steel clamps are preferable to the plain steel ones for obvious reasons. Don't over torque the screws, or you're sure to break that fragile 20+-year-old plastic. I would suggest going to Eurovan faucet while you're at it--nice upgrade. 

Troy