Barney, a few tips. If you want to go the sourdough route without it being too sour, you'll get better results if you buy the starter. Sourdoughs Int'l (sourdo.com) has several mild ones. A starter you develop in your own kitchen (for free) may or may not be mild, but probably not.
If you stick with commercial yeast, you have to chill between incubations because otherwise the bacteria will take over. Not even daily use will prevent this; in fact, most sourdough starters are pared back and rebuilt daily. By incubation I mean the period at warm temp when you're letting the yeast reproduce. For my experiment, I'm using four hours. Don't think I would consider going more than six. Bear in mind you just need the yeast to double.
As for coordination with your recipe, my strategy is to size the starter to make that easy. For example, I'm going to be using this starter in a simple sandwich white based on 450 g flour (1 lb, about 3.4 c by the stir-scoop-and-sweep method) and 300 g water (1-1/4 c). I prefer starters with a 2:1 ratio by weight, so I set up this one with 240 g water (1 c) and 120 g flour (just under a cup), plus 1 tsp dry yeast. Ran four hours, stirring down halfway through and again at the end, then chilled. Next day, discarded half and replenished with 120 g water and 60 g flour (no more yeast). Lather, rinse, repeat.
When I go to bake, the half I've been discarding is what will go into the bread. I know that's 120 g water and 60 g flour (scant 6 tbsp by volume), so I'll adjust the other quantities accordingly. For your bread machine recipe, you might need a slightly larger starter, but the principles remain the same.
Hope that helps.
ETA: I'm doing the pare-and-rebuild thing for two reasons. First, I'm curious whether this is a viable long term strategy. Second, I'm trying to develop a mild bacterial culture. If this works, not yet tested, the discards could have been used to bake all along, but I don't have the time, nor the need for that much bread.