From my limited experience, I can recommend that you don't buy anything made by Benning. We have one of their chargers at work, it's a modular rack mount unit and it's probably a touch over five years old. It has hot-swap rectifier modules, and they seem to be forever failing and being sent for repair.
On the other hand, we have four or five other chargers of similar output (~150A @ 28v) that are subjected to the same level of use and abuse, they're at least 15 years old and I've never been called to a fault on any of them. Can't recall who they were manufactured by, they might have even been a custom build. All the charger needs to do is output a set, regulated voltage and the rest will take care of itself. However, this is not the right kind of charger if the batteries may ever become depleted, as the charge current can easily run away when the difference between charger and battery terminal voltage is high. Of course, this should never occur in a pure float charge application!
I assume the genset uses lead acid batteries? If that's the case, I'm not 100% sure the concept of 'trickle charging' exists, you'd probably be referring to a float charger. This is where the charger holds a constant output voltage a little above that of the cells, and a very small amount of current equal to the cells internal self-discharge rate is provided in order to keep the batteries charged. This is pretty much self regulating, in that once the battery is at nearly full capacity, the charge current will diminish until only just enough is being drawn to keep the cell topped off.
If you may want to charge the battery from flat then you should consider a three-stage charger. These usually start with a constant current (bulk) charge of, say, C/5 Amps, up until the voltage at the terminals reaches a set point. After this it'll switch to a constant voltage (equalisation) charge and wait for the charge current to reduce to a set limit indicating that the cell is nearing full capacity, and then finally move onto a lower voltage to provide continuous float charge.
As you say, it would be wise to have the charger's output disconnected when the set is running.