Ok, solution-oriented with a budget, but young hardworking hands. The roof of the conservatory has rafters. They will be doubled in-house to about 20cm. Check if there is a membrane under the roof tiles. The wood must of course be removed beforehand. After doubling, insulate. Then a vapor barrier, cross battens, and cladding. There are many different variants, use the U-value calculator to calculate. Then remove the paving and build a floor slab yourself. Pay attention to the different and necessary levels and the wall connections. You can find all this via search engines. The windows remain weak points - that's just the way it is. Then you have done a lot with little money. Note - all in-house work, of course including reinforcement, concrete, and screed. I would then make the door to the "hallway" a side entrance door. Insulate the house roof in-house. That brings a lot for little money. About 30% of the energy is lost through the roof if it is not insulated. Then: look for weak points. Leaky windows, shutters, etc. If there is no new heating system, at least optimize the existing one. You can also insulate that, as well as the hot water storage tank, if present and old. It will all work out!