mit Aufwand bin ich mir nicht ganz sicher ...

I think you might mean:

"to keep costs down"

"to keep costs as low as possible"

costs - auch wenn es nicht im geringsten mit geld zu tun hat?

overheads?

keep outlay (or costs) to a minimum

"at" or "to"???

if it's fitness exercise: to keep the exertion to a minimum.

Candela, as you rightly suppose, Aufwand can mean expenditure of effort if that fits your context better.