More than happy to be corrected as correctness is not assured
the reasoning for running a pump is to give positive fuel pressure to the APU fuel control unit to preserve its lifecycle. Which pump you use depends on fuel load and flight deck occupancy by a pilot because as far as I’m aware, there are limitations to running centre tank pumps without anyone in the cockpit.
As a standard, #1 Tank is where apu fuel feed comes from, that is, the left side of manifold/crossfeed.
standard pump used is #1 Tank AFT. used for the feed in low range fuel quantity config’s.
Alternatively, some people use #1 Tank FWD - the benefit here is that when the #1 tank quantity is less than 1990kg, and there’s a bit of fuel in the centre, the centre tank fuel will be scavenged. This works best when you operate the classics as well as NG.
The centre tank L pump is used where fuel loads are greater than roughly 9tonne and can be run where fuel in the centre is greater than a specificied quantity and the cockpit is occupied. This is to prevent imbalance in the wings which I’ve seen once in 10years (easily fixed as long as it’s caught).
the right side of the manifold/crossfeed can be used and behaves in exactly the same way, except you have to open the crossfeed and remember to close it.
good luck with your training! There is a terrific 737 website which is tantamount to being authoritative, but isn’t. It’s website address ends with .org.uk if you google it.
have a read.