As far as leaving the lines on the dock and grabbing them, that would work for the home dock but we like to visit other places.
We like to visit other places, too, but your original post seemed to be focused on your home dock so I went with that.
Some marinas that we visit have pictures of the docks on their websites or a line drawing of the configuration. We like to look at these ahead of time to prepare a strategy if we can and if we get a slip assignment ahead of time, all the better.
Most of the time which line goes on first doesn't change much but it really depends on the dock configuration, wind and current at each individual dock. What we do sometimes when the lines are on the boat and the dock has cleats, is to use the boat hook to take a turn around the cleat on the dock and tie both ends of the line around the cleat on the boat. This way the lines can easily be adjusted without getting off the boat. Once we have the lengths the way we want them, we tie off on both cleats as normal. While the engine is warming up to leave, I do the same in reverse. Untie the lines on the dock cleats, take a turn around the cleat and tie the other end onto the boat cleat. Once we're ready to leave, I can undo the lines from the pilings but the boat is still held with the lines with the turn around the cleats. I then get on the boat and I can undo the lines on the cleats simply by taking one end off the boat cleat and swinging it away from the dock cleat.
It's much easier than that reads.
And then, of course, some marinas have people to help with docking so that helps, too.
I think it's good to be a little nervous about each docking situation. It keeps us cautious and on our toes.