We considered what you are planning OP but we also did a single storey out the back too… We’re a typical London terrace, at the end of a row.
One reason we needed to convert the attic before doing the kitchen extension was the scaffolding would have been much more complicated, and thus more expensive, afterwards. I wouldn’t do the single storey on the side and the second floor later - it sounds like a recipe for disaster. You’d need to find a builder in a few years time to quite literally build on someone else’s work… Agree with PP about trades being hard to come by currently!
We had planned to just do that hip to gable on the attic conversion, and make watertight, but not board out etc. until later. Due to a miscommunication with our builder he went ahead and fitted this out as far as first fix electrics (plumbing also in but no bathroom fitted) before we’d realised. He muttered something about not being able to get building regs without the attic being fully complete.
Like yourself we couldn’t afford to pay someone else to do it all. One way we’ve saved a large chunk has been to do all decorating ourselves (skirting boards, architraves, all woodwork and doors, prep work of walls and ceilings, mist coating plaster walls plus the usual painting) and fitting out of bathrooms. Might that be an option?
Also consider things like will you need a full rewire? Where will your boiler/gas meter/switchboard/underfloor heating manifold/water softener be located? Are you wanting underfloor heating (water or electric?) and how will this tie in? How does phasing the works impact on all of these? How will you ‘bring on’ things like underfloor heating and radiators once you tie these new areas into the main house?
Plan everything to the nth degree - I even knew where our Christmas tree would go. You need this so when the builder tries to bung the soil pipe, or whatever, down the middle of that wall you can tell them that doesn’t work for you as it’s the only place your grand piano (!) fits! Of even more importance if you’re planning to phase sections.