Did the trip a few years ago, and it's one of the best one's in my log book - right up there with flying in Hawaii!
Concur with Tinstaafl - Tingwall's a better option for Lerwick, definitely not as expensive and usually has AVGAS, from what I remember. Having said that, if you do end up in Sumburgh, IIRC there was only a landing fee. I made sure that I flew over Muckle Flugga lighthouse - the most northerly point in the British Isles - another tick in the logbook
Fair Isle is definitely worth a look too - It's a reasonably challenging strip in some conditions, and make sure you ring Dave Wheeler before you go; a really pro-aviation bloke who supervises the airstrip as well as being the National Trust bod on the island.
http://www.fairisle.org.uk/egef/index.htm
As for survival equipment - it's your call. IIRC it's about 20nm legs from the north end of the Orkney Islands to Fair Isle, and again to Sumburgh. Life jackets at minimum, but that far north, the water's likely to
feel very cold, even in mid summer.
You might also want to consider a quick hop between Westray and Papa Westray either on your way up or back. Shortest scheduled air route in the world!
Enjoy!
AA