How to get the "max" from two inputs?
I would do an OR gate with diodes. Each input has a series diode and the output of the diodes goes to a pull down. If any voltage is high the output if high, if both are low both diodes do not conduct and the input is pulled down.

Regarding the type of diodes, it depends on the other parameters of the design. If possible, I would use Schottky diodes.