Hi look up timber merchants in your area for the wood and hardware store for the screws, hinges etc, these will be much cheaper than the big diy shops.
Problem I see is some of the timber may need to be planed to shape or rebated to match the profile of the original for it to look right and fit together well. You'll either have to do this yourself or get in a professional if it's beyond your diy capabilities which it sounds like it may be. A local joinery shop may be able to source and profile the timber for you if you take the rotted sections to them for matching. The alternative is to carefully cut out the rotted sections treat the remaining timber and patch it up letting in new timber as required, there are some excellent fillers available today which you could then apply and sand to shape once set but you would need to then paint the whole structure for it not to look unsightly. Unfortunately timber and the british climate do not go well together and constant treatment and maintence is required hence the use of cedar or hardwood in high class structures and the rise in Aluminium and UPVC products.
hope this is of some help