I have just spoken to an experienced tyre fitter, so I thought I'd share the response I received:
If the size/ratings of the 'non-run-flats' is identical to the 'run-flats' they replaced, then the new tyres should be inflated to exactly the same pressure as the run-flats they replaced, i.e. the recommended pressures shown on the plaque in the car's door jam. (Obviously if for some reason this then results in tell-tale uneven wear patterns, for either over or under inflation, then the pressures should be tweaked accordingly).
Most emergency tyre repair kits (the through the valve gel type kits) will fix most punctures (other than side wall problems) and allow the car to be driven to a garage to sort the problem, but in 99% of cases these kits will effectively ruin the tyre and require the tyre to be replaced (not ideal if the tyre is relatively new). I was therefore told the best solution was to just have decent breakdown cover (which I thankfully do), meaning you can either be towed to somewhere to fix the tyre, or apparently these days the AA and RAC often carry a number of different sized donuts that they'll fit, then follow you to the tyre place, and then remove.