Shetland has become one of my absolute favorite places (I am returning later this summer for a vacation. If I could figure out a way to relocate there permanently, I would.)
There's extremely helpful information on the Shetland tourist's board
web site, and you can pick up printed copies of the brochures at the airport or in Lerwick at the tourist office.
You should definitely rent a (or if traveling by ferry, considering bringing your own) car. There are buses, but your mobility would be very limited and they are not so frequent. Details about the inter-island ferries are
here. You can call ahead to book a place for your car, but last summer (at the height of tourist season) we never had a problem not getting onto the ferry, so in general it doesn't seem necessary.
Your flight options are with Loganair or, apparently, after September 1 with Eastern, which will be codesharing with Flybe. I would recommend having good travel insurance to cover any pre-paid bookings in case your flights are delayed, as is not infrequently the case with flights to and from Sumburgh.
I'll be taking the ferry to Aberdeen in September, so can report back any notable experiences then.