I'd imagine it might be more expensive overall than a single project but I can see the logic. If you put the stairs in first you would probably need to have some way to close off at the top at the same time, otherwise it would be cold and dusty. But you could then leave the rest until another time.
The only issue might be if you could move in the next few years and buyers might be put off by an incomplete job.
Oh, and get planning etc done first else you risk getting turned down when you have started work.
We can't afford the whole job, but have got a small amount of money coming our way. Our neighbours with exact same house have had their loft done and I can see the stairs and where they are and it would help so much just having accessible storage.
We have no plans to move as we can't afford to. Would we need planning permission for a loft?
Unfortunately from a building regs point of view the permanent stairs are the one thing that usually classes it as a loft conversion rather than storage. So you can do whatever you like up there in terms of partial conversion, but as soon as the stairs are done it should all comply with regulations. From a practical point of view you'd need to do the structural work first to avoid having to redo the stuff you already did. So steel beams and floor joists basically. Insulation can be added later.
With a job like this, there are bits that are more do-able by a competent DIYer, and bits that you really should leave to a builder unless you're shit hot. I would get the latter done with the money, and then do the rest yourselves. Things like boarding and insulating a loft are time-consuming, but not that technically hard. What you do need is to have an extremely clear plan, which you know meets building regs - otherwise you can end up making very expensive mistakes.