I have done all of the above in the past, trying out what I’ve read in various places or heard on podcasts. My current practice is to make an oxygenated starter (sort of SNS) the morning of brew day and pitch once active. I like the results and can count on the results so much that it’s what I do solely now.
I found that FOR ME washing/rinsing yeast did nothing. I’ve tried it various ways. I think there’s some validity to the idea that storing rinsed yeast in water is not ideal for ph reasons.
I gell fine in primary, and my concern used to be the settled gelatin. If I were to repitch I would simply take a small 100ml portion and build my normal starter… gelatin doesn’t reproduce so that would be a decent way to limit transferring it to the new beer. Dry hops and trub too for that matter. I have repitched en mass before, and no doubt many people get great results. I am an outlier who just prefers my starter routine.
Storage-wise, if I went back to it, I would store in a sterilized container on the original beer in a fridge for up to 6 months, using as sanitary transfer methods as I could, and I probably would limit my repitching to about 3-5 generations. Less if I started experiencing any changes in the beer.
After I keg, I swirl the remaining contents in the fermenter, wait 5-10 minutes and then fill a sanitized 24 oz jar (spaghetti sauce) all the way up. I put that in the fridge with lid loose. After setting there is about 8-10 oz of yeast slurry which is a lot for my 3 gallon batches.
Next brewday, I usually just decant and pitch the slurry directly into the wort. I usually use the same yeast 2-3 brews in a row, so, the stored yeast never gets very old.
The settlement in my yeast jar has trub, bits of hops, etc. but, it seems to work.
I don’t worry about what was brewed before with the yeast. I don’t think there is enough matter there to make a difference. Then again, I don’t brew extreme hoppy or dark beers, so maybe this is just not a concern for me but could be for others.
I’m pretty basic with mason jars in the fridge. Like Jim, I’ve done pretty much every variant.
These days when I buy a new strain I like to make a starter larger than what I need for the first batch and send the extra portion to a mason jar so I have a clean slurry. I may or may not harvest slurry from batches of beer. I can always make a starter out of the clean slurry and repeat the process so there’s always clean slurry in the fridge and healthy yeast going into beer.
I have some mixed cultures as well. These stay in mason jars in the fridge as well. Periodically I take them out, pour off some of the liquid and add a little fresh wort. I’ll leave it at room temperature for a day or two with the lid loose. Then I seal it up and put it back in the fridge.
Plastic lids for Mason jars are great. Don’t order on Amazon where they are oddly overpriced. They are a couple of bucks at Target/Walmart.
The plastic used is a bit brittle when cold which I find odd. Found this out when one split open after getting knocked over the the fridge. Maybe it’s just too thin.
Palmer has always said he uses Mayo jars, but I’ve never been able to get the smell out.