"I would recommend doing both elapsed time, and step counting."
I would agree with that with one caveat.
There is no real time clock/calendar (RTCC) hardware on the board.
So if you ran it for an hour, let it sit for a month and turned it on again, the very best you could have tallied up would be that one hour.
I don't think that is what you are after.
I have designed lots of hardware with RTCCs present.
My favorite RTCC chips are the MCP794xx series (I2C interface).
They have an additional couple of neat features- they have the ability to tell you the last known power down and power up times, and a couple of them have unique serial numbers which might be useful.
But as long as you go to the trouble to add the interface to talk to it, you might as well also add a serial memory chip such as the 23LCV1024.
That would give both RTCC and battery-backed RAM (infinite read/write) memory functions and would make what you suggest doing trivial to accomplish.
There is a little read/write memory in the RTCC chips, but my experience with it has been spotty.
Better to add a dedicated RAM memory device.
Truth be known, there is probably already an RTCC add-on card for Arduinos out there. Just buy one and wire it in.