Already so many comments so I thought I should post this before I spent the rest of the night reading them. Only the other night I was thinking about this but more precisely what order then I realised the best way to visualize this is to get my crayons out and draw a map. So here it is...
Kettering to Sheffield since its the third mainline and would be politically silly to do anything else before it! Also part of it is needed for HS2. Then I would carry it on from Sheffield to Leeds via Barnsley and Wakefield Kirkgate. It is city to city and Barnsley and Wakefield are both heavily deprived areas! At the same time I would wire Horbury to Ravensthorpe so that it could connect onto Huddersfield once the TRU section has been completed and from Normanton to Church Fenton that should be wired by this point. After that I would continue it through Leeds to Harrogate. Its a busy line that could be integrated with the Shipley triangle services.
Then I would do Sheffield to Doncaster, Doncaster to Gilberdyke via Goole. Before Selby from the East side of the Swing bridge to Hull. This way any temporary closures and services could terminate at Selby, also this gives some time to work out how best to wire the Swing Bridge that is a bit of a sticking point. Then Leeds to Selby followed by Bradley Jct to Todmorden. By this point I would have wired in Lancashire...
Manchester Victoria to Rochdale, put a few more platforms in at Rochdale to free up platform space at Victoria, Blackpool South - Wesham, its single line running through heavily built up areas for about 20km, then I would do Preston - Colne, some big populations and not a single tunnel I believe. At the same time Bolton to Blackburn, since Bolton is already wired. Before the Burnley to Rochdale via Todmorden.
Back to Yorkshire I would then carry the wires on from Milner Royd Jct near Sowerby Bridge to Leeds via Bradford Interchange!
Ive tried to do it in a way that delivers the most economic benefit, but also in a way that naturally follows one another. Also by the ones that are easier to do with the least amount of disruption hence why Halifax is near the end.