Cardschat has all the answers to your bankroll questions.
https://www.cardschat.com/poker-bankroll-management.php
There is a lot of good advice in that article but also some, I disagree with. 20 buyins for cash games and 50 for tournaments is very aggressive and frankly outdated. 30 and 100 are more reasonable number to go for in todays tough games. Maybe 70 for single table SnG and 200, if you only play large field MTTs.
And for cash games the bankroll requirement must be defined from the table maximum, even you buy in short. You are much more likely to be all in with 40BB than 100BB, so playing short does not reduce your variance proportionately. Playing 10NL with 80$ bankroll will almost always end in tears. A beginner with that bankroll should be playing the 2NL tables instead.
I also don’t agree with the advice to not use auto top up. I understand, that the article is written for beginners, but why not learn good habits from the start? By not using auto top-up you need to constantly adjust to different stack sizes, which makes learning more difficult.
Sure its relevant to track your results and follow a stop-loss strategy, but you can track your results in the cashier or in your tracker, if you use one. Also if you use more conservative bankroll management in the first place, its less of an issue, if you somewhat exceed your stop-loss.
I also dont like to set a stop-win. When we are winning, we are typically playing well, and maybe we found good tables, so why not make as much as possible from that situation? It makes a ton more sense to cut the session short, when we are losing. Keep your winners and dump your losers is an old mantra for stock investors, and poker players should generally be thinking the same way.