Upvote:4
Airport
If your goal is Scotland than yes, go straight to Edinburgh. London deserves some time to visit, if, with your question, your implying that you could spend some time there.
Period (7 days)
That's allways a bit subjective. You can always spend more time in a place. I would say that, for the itinerary you want, that is the minimum comfortable time span.
Itenerary
Quick notes:
Edimburgh is a very nice city, you can easily spend there 2~3 days.
Inverness is nice but small. You should think of it more as a good departure point than for the city itself. From here you can easily reach the highland lakes and the islands, in particular the isle of Skye.
If I had to make an itinerary based on your information I would do it like this:
(It's up to you to decide where you want to spend more time and manage those days. The days mentioned are just a reference).
Transport
Train is nice but more expensive than Bus. If you're lucky you can get very nice prices with MegaBus.
It might be a good idea to rent a car in Inverness.