Personally I see the South stand being done first. My rationale is that we currently have segregation issues on the away end and G and H of the South stand and John Street, that can be resolved if we have more seats.Many fanbases in the Championship or Premier League would take up full allocations, if tickets were reasonably priced, in a similar way to that they used to be on Leppings Lane, Swillsborough. We also do not then need to consider giving blades fans tickets on the Bramall Lane end ,as they would be provided for on the extended new South. The South stand regularly sells out, even in league one, as well as the corporate facilities on John Street. These punters pay more for attendance than those on the Kop, so the business plan would be sounder - so long as we stayed in the Championship or Premier league. There is currently more of a need to provide higher priced tickets, corporate facilities and access all the away seats, than there is to provide better facilities and cheaper seats on the Kop. There has been an interesting debate, with some similarities, at Anfield in the last few years. They decided that their new main stand would mainly cater for higher paying fans, rather than those on their 25k waiting list, as the stand would be paid for in five years. It would also keep demand high for high cost tickets due to there being more demand for all tickets than is met by the current supply. The Liverpool owners will not improve their version of the Bramall Lane end (Anfield Road) as the business model doesn't stack up. The price of general admission tickets, in a stand with no corporate facilities, does not add up and would require a long term loan.
This all presupposes that stadium renovations are being considered as investments, not just a gift to the football club. It also doesn't factor in other revenue streams that could be accessed by renovations of the Kop or South stand.