I'm trying to "force" some of the npc's around my characters house to look like Vigilants of Stendarr, but how can I do this without the change each time I come back or exits the game and start it again?

I have tried the "Equipitem" command, but the keep changing back to their armor.

NPCs that have a "default outfit" set will always revert to that outfit when they are not your follower. You cannot permanently change their clothes with console commands. However, you can use the Construction Kit and just change the NPC's Default Outfit, or use the Skyrim NPC Editor mod to do the same thing.

If it were me, I'd just edit the NPC in the CK. Just go to the Inventory tab and either set the Default Outfit to "NONE", or set it to one of the three pre-defined Vigilant of Stendarr outfits.