The rough summary is "you need to keep enough details to be able to prove you/amateur built more than half of the plane to certify it as an amateur built aircraft".
You can use paper and photos or an online blog or anything in between.
So just one key thing - not just pictures of the parts, but also proof that an amateur built it (such as pictures of you in action).
At the end of the build, you have to submit an Affidavit to swear that it was majority amateur built and if the DAR has any doubts, then you have to be able to show sufficient proof.
As for my setup - I have my blog where I write up my progress with many pictures and then I also have my timelapse camera in the corner to document the progress and show it's me building it.
The camera I use is a
ZeitDICE, which is specifically for capturing timelapses like that, so the battery lasts very long as it just takes a picture at X interval - I do one picture every 10 seconds while I'm building for the videos you can see on my YouTube.