Start building the parts. I recommend building the starting lifting mechanism first. This way if you run into any problems or if your measurements are off then you will be able to adjust the rest of the track from the beginning.
I highly recommend not working on parts of the track on all walls at the same time. If you mount track and different elements on the different walls and the tracks don't meet up as you join them together then you may be removing pieces to adjust them up or down. This may mean a lot of wasted time and possible patching of holes in the wall.
One thing you want to watch for is that as you add your track is that the height of the track on the wall is not lower on the wall than what you estimated. This can cause problems as you work your way around the room and you realize that the track is now lower than expected and is now in conflict with doors, windows or other things that you don't or can't move.