Welcome to the Forums, Steve!
In a nutshell, you need a 700c rear wheel with a 19mm wide rim (or as close as you can get to 19mm). The important thing is to also count the number of sprockets on the rear wheel, and make sure that the hub matches the number of sprockets (8 speed or 9 speed).
If the tire itself isn't cut or otherwise damaged, then it should be fine. As you surmised, you need a 700 x 35 to 43mm inner tube. Tubes are designed to fit a range of tire sizes, so don't let that throw you. Make sure you get the matching valve, both for the tube and the wheel. If your original wheel has the larger Schraeder valve instead of the narrower Presta valve, the new wheel can be drilled for the larger valve.
All of the other numbers (622 x 19) are International or Overseas equivalents; the important measurement is the 700 x 19 rim, and the 700 x 42 tire & tube.
Hope this helps!