My first trip to Orkney was about 15 years ago. We took a ferry from Scrabster to Stromness and took our rental car with us. It was very easy and worked out well since we were driving up from Skye. We spent four days on the mainland, which gave us time to see everything we wanted to see, but not enough time to visit the other islands. Well, we could have squeezed in a day trip to one of them, but we had torrential rain on one of our full days there.
This past July we spent about a week in Orkney and a week in Shetland, which gave us time to visit several other islands. It was pretty close to ideal, but I would have enjoyed another day or two for each. I think eight days on each would be wonderful.
On our most recent trip, we rented one car in Kirkwall and another in Sumburgh. We mostly flew to, from, and between the islands, but we also took the rental by ferry to a couple of the islands. We traveled independently, but the arrangements were made by McKinlay Kidd. They are a travel agency that offers small group tours and independent tours with and without a car rental. You might want to google them and take a look at the tours they offer. You could get ideas on planning your itinerary even if you don't book with them. We did the Complete Orkney and Shetland tour, which we thought was fabulous. They booked all the flights, ferries, hotels, and car, as well as some full and half day guided tours (both group and private). They also offered suggestions on what to do during our free time which was plentiful. We loved using them, especially since planning the flights and ferries can be a real pain in the butt when there are not that many options and coordination is critical. Please note that you can tweak their tours or have them plan custom trips. I thought they were fantastic to work with, and the cost was very reasonable.
As for flight vs ferry, I think either is fine, but flights are faster, which is a plus. We took seven flights and all seven were on time or close to it. You may not be as lucky, so follow Pam's advice to build some slack in your schedule to allow for delays.
We started on Orkney and then went to Shetland, which I thought was ideal. Orkney is a little less populated and remote, and I prefer to transition from city to remote countryside gradually. I don't think it makes that much difference though, so I would go with whatever fits best with your overall itinerary.
It sounds like you have a fabulous trip in the making. I can tell you our Orkney and Shetland trip was one of our all-time favorites. It was magical! I love all of Scotland, including Skye and Edinburgh.