Here's a website that sells parts for old machines. I think it's where I bought a leather replacement belt for my cousin's treadle:
http://sewingmachine221sale.bizland....re/page47.html
Here is a website and list for White treadles I remember from years ago:
http://www.treadleon.net/. (The Captain is easy to remember!)
For cleaning, a lot depends on its condition. Be careful not to scrub too hard or use abrasives, as these can damage the finish. Most people recommend wiping with a damp cloth or a soft cloth and oil (baby oil, I think, or sewing machine oil). Oil will loosen dirt and not damage the finish, but I would probably use a mild solution of water and dishwashing liquid afterwards to remove the oil.
Speaking of oil, you want to get sewing machine oil and put drops in all the oiling places -- both on top and bottom, plus any moving parts you see. Do not use any other type of oil, as sewing machine is extra refined and nothing substitutes for it.