Start with deployment, because it is the easiest to settle. Unless you have a specific data residency obligation, a heavily customised legacy estate that cannot be re-platformed economically, or sites with genuinely unreliable connectivity, cloud is the answer and the rest of the evaluation gets simpler.
Then size the requirement honestly. Count entities, currencies, stock locations, manufacturing processes and the number of people who will actually transact in the system rather than read from it. Those five figures separate mid-market from enterprise far more reliably than headcount or turnover.
On generic versus industry-specific, look at what the sector product does that a configured broad platform cannot, and price the difference against vendor risk. In our experience most UK mid-market requirements described as unique turn out to be configuration, not product selection.
Finally, test growth. The most expensive ERP decision is not the one that costs more, it is the one that has to be repeated in three years because the platform ran out of room.