You want Celotex type insulation, its rigid board with foil both sides.. I used 75mm stuff on the shed I pictured above. 4 (95mm) stud walls, which allows an air void to stop condensation forming in the cavity.
You need to go to a trade builders merchant. Dont bother with Bodge It & Quit (B&Q) or any other diy place.. The builders merchants will be a fraction of the price. If you want it to last and be sturdy use 3x2 (4x2 will be better) sawn treated timber for the walls, studs spaced at 400/500mm. Depending on the span, you want 5x2 minimum for roof. If flat roof forget the old roofing felt, its old hat.. Iv been using Fibreglass roofing system for the last 5yrs. Its a lot nicer finish, it has 25yr guarantee, it is slightly more expensive, and it is a bit messy, but its worth the cost and effort. Take a look on eBay and find the biggest bit of double glazed glass you can find for the cheapest price, use it as a roof light..
On the walls, use feather edge boards on the outside, and 9mm or 12mm ply on the inside. Fix the boards with 30mm screws every 6 to 8 and it will negate the requirement for diagonal bracing. You should really use a breathable membrane(modern day roofing felt for conventional pitched roofs) on the outside before you fix the boards.
The other option, which is cheaper, is to build it with concrete blocks. The only trouble is you may need planning permission depending on size. Timber structures come under different rules because they are not considered perminant.