Re: Shutoff valves
It sounds as though the angle stops are not completely closing, which is quite common. In cases like these, it is necessary to turn off the water main to the house. At this point it is in your best interests to replace the old angle stop with a new unit, preferably a ball valve that does not suffer the same problems of a standard "screw" valve.
I would recommend replacing the angle stops first, then proceed with your other repairs/replacements so that the water supply to the house isn't off for any longer than necessary. Plumbing issues can easily take far longer than initially anticipated, you don't want to open things up and not be able to complete the job. Get the sink isolated first, then continue with your repairs.
I suffer from CDO ... Its like OCD, but in alphabetical order, LIKE IT SHOULD BE!!!