When you validate your project the settings in the Connection matrix comes into play:
It can't catch all the errors you make but it might save you from some mistakes. I would set them to Power, then check any warnings I get. If the warnings and errors were just annoying I would set the pins to Passive.
If you want to use theese properties depends on your design environment. If you're a single inexperienced designer, you might want some extra help from the tool. If you are an inexperienced designer in a big team you might waive the ERC warnings and let the review board catch the errors. An engineer with many years of designing might find the Altium settings a nuisance and set everything to Passive because the errors the ERC can check (and generate) doesn't add any value.
Regarding simulations, I have never used Altium for simulations. At all the places I have worked the simulations have always been done by recreating the circuit in another tool, Hyperlynx, LTSpice etc.