I believe the ideal set up is a diaphragm pump set to the lowest pickup point for all convenience pumping, ie. to remove shaft drips, fridge or a/c condensation or other acceptably minor bilge water. Then place a centrifugal crash pump, just slightly above it, in the event you have a serious ingress and need maximum gph.
The diaphragm pumps will inherently prevent backflow, but are usually low volume pumps. The centrifugal pumps don't hold back and it's well known that check valves fail (open and shut, both bad). No need for a check valve on a crash pump hose anyway, it should never have water in it.
Last couple of basics.... be sure to use smooth bore hose to allow for the least amount of flow loss. You may need a loop up to the deck level to prevent a back siphon, when heeling. This can reduce flow, as every pump loses capacity, for head rise. I only use pumps with separate float switches, as the switch is the most likely to fail and I don't like having to replace the entire pump, because of the switch. It's possible, this is exactly your problem. With separate switches, you can also keep both pumps (or their pickups if separate) at the bottom of the bilge and just stagger the height of the float switches.
I also think a high water bilge alarm is a cheap and easy to install safety item too.
All good advice, IMHO. However, sometimes your bilge configuration dictates compromises. Minne’s strategy works if you have sufficient bilge depth and volume. In my case, the bilge is divided into 10 very shallow (3”-6” depth) sumps that are not connected by limber holes.
My primary bilge pump is in the engine compartment that includes the shaft seal. That is the only area that has seen seawater and once overflowed into the main cabin bilge areas when a new pneumatic switch failed. That switch was replaced by an electronic switch that provides for an easy test. However, the high flow centrifugal pump is a tight squeeze and could not be directly replaced by a diaphragm pump (like my secondary bilge pump further forward).
I could locate a diaphragm pump about 5’ away from its pickup to catch the minor amounts of water, but the bilge pump has only been called to automatic duty twice in 22 years, and neither occasion involved a massive influx, so I think I will stick with the centrifugal pump, electronic switch and check valve in the 1 1/2” output hose. Periodic checks should suffice to verify that the check valve and switch are operable.
My main bilge water problem is the rain water that comes down the mast via the halyard entrance and exit holes. The photo shows the mast step and associated bilge areas. The head is to the left, wherein is located a diaphragm pump to handle the shower sump and act as a backup, manually-operated bilge pump. That pump is on a Y-valve that supports a 12’ x 5/8” “central vacuum” hose that I can use to pump out the numerous compartments in my bilge—primarily the area by the mast step after a heavy rain or two. There does not seem to be an easy way to automate the rainwater removal.