You might find this useful....
www.shetland.org/60n/blogs/posts/shetland-rapido
It looks at a three day trip, though the second day is more rushed than is ideal. It’s a wonderful time to be in Shetland, as it doesn’t get properly dark; the day just fades to twilight.
There’s lots of information elsewhere on the same website. You have the choice of flying from Edinburgh, Glasgow, Aberdeen or Inverness. There may be some advantage in choosing Aberdeen, as if there’s any problem with a flight (eg summer fog, though that hasn’t been so much of a problem in the past two years) you can transfer to the ferry. Flights are operated by Loganair and the least expensive seats go quickly.
The ferry runs from Aberdeen every night, at either 5pm (when it goes via Orkney) or 7pm, getting into Lerwick at 7.30am. The ships are fine, but it’s best to have a cabin, which are 2- or 4-berth. The Scottish Goverment has said that a new fares system will operate from this year, reducing the basic fare and the vehicle fare, possibly by about 30%, but details are scarce so far. There’s no price advantage in booking early with the ferry, but you might not get a cabin if you leave it too late.
Even when/if the fares reduction kicks in, bringing a car for a short visit may be more expensive than local car hire (Bolt’s or Star). It is possible to get around by bus, but you’d not see nearly so much.
As to accommodation, I’d check TripAdvisor. The Scalloway Hotel, Burrastow House and Busta House are good; there are good B&Bs too, and there are budget options including an excellent youth hostel in Lerwick and ‘camping bods’ (bunkhouse-type).
Hope that helps.