If I understand you correctly, you are talking about a northbound hike of the entire JMT starting at one of the Horseshoe Meadow trailheads. If so, then my preference would be Cottonwood Pass most likely. I’ve only personally done that route, so maybe Cottonwood Lakes up to New Army Pass has some positive reasons recommending it, but my understanding is that Cottonwood Pass is a little easier over all. That might be nice at the start of such a long hike.

You can definitely summit Whitney from the West with the regular overnight permit as long as you descend back to the west and continue your hike along the JMT. As mentioned in an earlier reply, if your intent is to summit Whitney from the west but then exit to the portal, you will need the Exiting Mt Whitney version of the overnight permit. This is MUCH harder to come by in my experience.