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.
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:
- Edinburgh (2 days - don't forget to visit the world famous Greyfriars Bobby and greyfriars cemitery... ... I leave it up to you to discover why).
- Glasgow (I haven't been there) but I am sure it's worth checking (0 or 1 day maybe?)
- I would definitely stop in Fort William. It's very beautiful, specially if you like the outdoors. It has some amazing trails near by (1~2 days). It's a ver nice place for camping if you enjoy it.
- Follow the lakes (caledonian canal). You will pass Loch Ness (not the most beautifull lake but it's allways worth looking for the famous monster). After some more miles you're in Inverness. You can spend there half a day. No more than that.
- From Inverness you can go north to the lakes (1~2 days)
- And also to the isle of Skye (1~2 days) (Don't forget to stop on the Donan Castle :) on your way to the isle of Skye).
(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).
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.