Flushing the cooling system is never a bad idea, particularly as the heater matrix is so prone to blockages from sludge and debris. Air locks can be avoided by priming the heater circuit with a garden hose and purging it of any air. I tend to fill the radiator up first, then disconnect the heater inlet/outlet hoses at the closest point to the engine, i.e. the heater tap (or the thermostat housing sandwich plate on later models) and the bottom hose, then attach a garden hose to one, and a spare length of hose leading to a bucket to the other. Then gently turn the garden tap on until water runs clear into the bucket, before reattaching the hoses again. Don't turn the garden tap on fully though, as full mains water pressure is likely to damage the matrix. You'll then need to run the engine at idle, with the heater tap open, to allow the water in the heater circuit to mix with the antifreeze in the rest of the system. If you run the engine until it gets up to temperature with the rad cap off, then any remaining air left in the system should be able to escape, then top up the rad as necessary.
As for antifreeze ratio, as far as I'm aware it doesn't matter which you use, so long as you don't mix them. Most classic cars tend to use the traditional blue antifreeze and will continue to do so, as they have to top up with the same type from then on. Modern cars usually require the red/yellow OAT type, I don't see why you couldn't use this type in a classic mini if you're completely flushing the system first, but I'd get this confirmed before using it. As for ratio, this is somewhat dependent upon the type/brand you use, so check the instructions on the back of the bottle before diluting it. Most will recommend somewhere around the 40/60 - 50/50 mark, but that actually tends to give you protection down to something ridiculous like - 35 C!! In reality, with the types of winter temperatures we get here in the UK, you could probably get away with more like a 25/75 mix.