Water pump advice

[H2]

What is the best way to clear build up in the water pump?

Also when should you replace the water pump?

[Serious Series]

I would be more worried about what is in the rest of the cooling system than the water pump as that is easy to change. What does your radiator look like?
You can put some cleaner in and flush it dishwasher tablets will clear some of it but you may need something stronger.

[H2]

I've bought a new radiator. I'm trying to find out what I should flush the system with once it's attached, to clear out the old stuff in the engine block.

[Serious Series]

Have you still got the old radiator as it maybe better to fit that while you flush the system.
Central heating cleaner may shift it as it looks like too much for dishwasher tablets.
Fernox
Fernox F8 Super Strength Cleaner Boiler Central Heating System Sludge Remover Radiator Protector Inhibitor 500ml
or
Sentinel.
Sentinel - X800 Fast Acting Cleaner 1L, targeted central heating system cleaning inside an hour, restores system efficiency by targeting corrosion debris, ideal for hot and cold systems