Christine and I go for ten days every year, initially by motorhome, more recently in my Renault Convertible (As used by hairdressers everywhere). I'd say that you should:
Arrive Glasgow: Hire car, drift down through borders and lake district and hand car back in Manchester.
Take train from Manchester to Glasgow and hire car for trip round Highlands.
I know that it might be pricier, but I once mapped out doing the trip of the Highlands by public transport and it was only just doable and didn't leave any flexibility.
N.B. You can pick up and drop hire cars at main stations, as well as airports.
A few personal notes:
1. Glasgow is OK, but Edinburgh is so much more, it's our favourite place: we go about 3 times a year.
2. Each of those islands, I find disappoints: A long trip with not much at the end. We came back off Skye after half a day (Mind you it was sheeting down with rain). After all, you don't have to go to the Island to get the Whisky!
3. Oban to Skye, yes great: But Fort William to Mallaig by train: Much, Much greater (by steam, if you're lucky). If you are not driving it's better to look around.