Ah I was confused as to what the rules were and if it was permanent.
So taking your original suggestion/rule of 'Has to be from your immediate house/work' Here's what I'd take:-
One of the reeds that had formed the underlay for the tiles on my roof. It had lasted nearly a century and a quarter but had finally deteriorated by the time I moved in. I'd have liked to have them replaced with new ones but it wasn't my call and in any case I'm not sure how easy it would have been to find someone to do it. Not a skill that's in great demand these days. I wonder if the modern stuff will last as long?
Anyway I kept a bunch of them so I'd grab one to take back to the time it was being installed, maybe even going back a bit further to catch sight of it when it was still swayng in the wind prior to harvest. Then if I could get back to the house via wherever they were making the clay lumps to build the house with, that would be pretty cool
Then I want to see the first people to live here. And if there are no rules about how long we can stay and how quickly we have to come back I wish to come back in increments stopping off at each new set of occupants. I often think about them, particularly the ones who went through other times of national crises ie WW1 and WW2. I feel a connection and wonder if any of them had familly members away on 'the front'. I sometimes wonder if they can see me .... well I have a Fortean mindset after all so I like to play with the possibility.
I'm afraid I can't come up with anything more witty/imaginative/exciting than that but it is what I would do,
Sollywos x