At my last place, I installed a pumped shower because the bathroom was upstairs, leaving only a couple of feet head of water.
I used a Stuart Turner Monsoon unit, connected to a standard bar mixer.
This was installed in the loft, as low as possible below the cold tank, because the pump does need some positive head to operate.
You need to provide dedicated high capacity feeds to the pump from both the hot and cold water tanks.
You can't just tee it into any convenient hot and cold pipes that run nearby.
Eta: A pumped shower uses stored hot water.
Any shower that does heaty-up-on-the-fly needs a serious amount of power to provide a decent shower. Either many kW of extra-tickly (10.5kW was the biggest when I last looked, requiring 16mm2 cable which is unwieldy to work with), or from a gas boiler which will be in the 20kW+ range.