A pump should never have to work to draw water. There should never be any kind of anything on the intake side of the pump that would serve to constrict the flow in any way.
Return pumps are almost always either submerged in the sump water or located outside of the sump, connected to it with a short pipe of equal or greater diameter than the pump's intake, thereby drawing water from a free body of water. If you have multiple pieces of equipment you want to daisy chain, then they should all be located on the pump's outlet.
Skimmers are a different story because nearly all skimmers cannot feed water to anything above themselves. It's not like you can feed a skimmer with a pump under the stand, then run the pipe from the skimmer up to the tank, it doesn't work that way. I've seen skimmers that supposedly can do this, but they are of unorthodox designs. Skimmers are usually used in sumps or outside of sumps, but with the water returning back into the sump, rather than being pumped to something above the skimmer, or hanging on the back of a tank doing the same thing.
In your chiller example through, you'd have SUMP>PUMP>CHILLER>TANK, never SUMP>CHILLER>PUMP>TANK.