So, I was able to mount the fixture right over the old box.
The ground was already hooked up to the box where the fixture screw was. I used the spot that the ground screw was to screw the fixture right up to the ceiling and attach the fixture right to the box, while feeding the wires into the strip light. The power from the house had Red and White wires.
One screw got it right to the ceiling so I could mount the rest of the fixture with drywall anchors It even grounded the fixture as well. I got the $40.78 fixture with T8's, it claims to be instant start. Started right up during the smoke-test. An hour later and the house is still not burnt down!
Next weekend I'll do the shop area. It will be different because the box in the ceiling I want to turn into a couple outlets because I'm looking at some different fixtures that hang down a little more and plug in.