suggestions for a soundproof shed .
Firstly , if possible get shot of the petrol genny and get a lister CS gen set. . They run off diesel and will run non stop for many years with almost no major work on them . Old sets can go for about £500 now , but you can buy brand new ones ( listeroids) from India for about £1000. They will give you about 2.5-3 kva of leccy , more or less enough to run your house on . Plus they will run on ordinary diesel , red diesel , heating oil used engine oil , vegetable oil , and used veggie oil . The used oils have to be filtered , but the engine will run on all of them , or any mix of them .
They are much cheaper to run than petrol engines and run at a much slower speed . The average petrol engine would run at say about 1500 -3000 rpm , and the lister at about 650 rpm. They are also much quieter . A petrol engine genny , running 24/7 52 weeks a year , wouldn't make it through the first year , unless you had some huge power station type thing . But the lister's have been known to run for 25 -50 years non stop. Just keep topping the fuel up .
Anyway , that said ....sound proofing a shed. Well firstly sort a new exuast out for the engine . The little square or round lumps they have on them are crap. On this score you end up a bit Heat Robinson , cobbling up a car exhaust or some such type of thing . You can also dump the end of the exhaust into water , you then get that burble that boats do.
Sheds should be lined with something like fibre glass insulation ,sheet polystyrene ,or you can buy sound board , which is like soft MDF . Don't forget to do the roof . It acts the same as a drum skin , so insulate it well . Once again glass fibre or polystyrene will work if you don't mind using them . Sheep wool insulation would work well too.
The shed can be made of anything , dependent on funds , but make sure the genny isn't sitting on a raised wooden floor . Again it would act at best, like a drum skin , at worst like a stereo speaker.
A concrete base would be the best thing, the deeper the better. Or you could use hard core rammed, and then covered with sand and then slabs as the floor.
Loads of ways of doing it ... but the main one is get shot of the petrol genny asap ....way to dear to run .

cheers
Russ