There has been no previous "proper" shower installed in this house
(other than than something which goes over taps).

The house was built in the 60s, and has a hot water tank on ground
floor, and a cold water tank on the first storey (it's NOT in the
loft, its actually in a cupboard in a first storey storage room). The
bathroom is also on the first storey. The bottom of tank is about 1m
above the taps, and would be below any shower head. Saying this
though, the pressure out of the taps on the bath seem normal?

I am wondering what is the best type of shower to install, i.e.
electric/power/mixer etc... I saw in Argos croydex h20 which is a
mixer that supposedly works well even with low pressure, dont
understand how because it says it needs no electric connections or
pumps? I personally would have thought only option would be electric,
but how would the flow me?

I am also wondering how much one should be paying for this to be
installed, including all plumbing work, all electric work, but I would
supply shower myself.

What are better brands of shower, I think this group totally rules out
triton and gainsborough, how about showerfoce, creda, mira etc...

you require a min of 1 metre from bottom of cold tank to shower head for a
good shower.Go for a pumped if you can not raise tank