After feeding starter..... or after feeding and allowing it to double in size?
After it has doubled in size for more yeast activity compared to bacterial.
More important to be consistent. Enjoy!
It depends as many things do. If you’re planning to use it pretty soon within the week, I’d say let it peak first. Doubling for many starters isn’t at peak. Peak is the maximal rise and then the dome just starting to flatten.
If you’re keeping for starter for much longer than 1 wk before using it then leaving some food for the microbes while refrigerated is fine to do as well and in that case refrigerating prior to peak is good.
I like predictability in my starter and I find the second scenario isn’t as precise and consistent for me, so I allow my start to peak and then refrigerate. I want my starter to be predictable when I then go to build a levain.
I feed my two levains (one wheat, one rye) weekly. Once fed, they get around 5 hours on my counter at room temp, till I can notice a few surface bubbles with the white levain and bubbles on bottom and sides of the rye sour. Then I refrigerate. Been doing this for 15 yrs and they are both happy and healthy. I do make both somewhat thicker - more like a biga than a 100% hydration so that there is sufficient food for them to eat for 7 days if I’m not baking.