Aircraft suitable for zero g flight

I'm interested in learning to do a zero g manueveur as part of my aerobatics
training. I get the idea that this would require certain characteristics
from the fuel system, i.e. the fuel still needs to flow into the engine in
zero g. Will a standard fuel pump system as provided in aerobatic aircraft
be capable of handling this? Liquids in zero g have a tendancy to form
spherical bubbles that just float around, although surface tension still
works.

As for method of doing it, I would expect the best method is the old NASA
method of hanging a small weight from the compass, if the weight goes down
push forward, if the weight goes up pull back. Anyone done it? Thanks,

David