When I joined, Elder McNamara said I was now entitled to all the equipment, weapons, and ammo that all the others have, but where do I get it?

You can buy them from the store in their Bunker. Right next to the target range.

Plus if you help the armoury lady with something, you do get a weapon. You can also get access to their safehouse and the contents.

Grendalcat: Thanks, didn't know there was a target range ; it's underground? I thought I'd covered the bunker pretty thoroughly but I guess not.

David: haven't met the armoury lady, either. Will now travel to the safehouse, which I've been meaning to do, but there was no mention of weapons there. Good to know. Thanks.