My first reply was a bit short, so I like to add a few more points, because I think, this is a question, many new poker players have. Now first off all you need to define, why you are playing poker? Is it mostly for fun, or is it for profit? If its mostly for fun, then just play, whatever you enjoy, and dont lose money you need for something else. Make a budget but dont think about bankroll management, because its a meaningless concept, if you play for fun.
If you play for profit, you should still enjoy playing poker, because otherwise you will quickly end up hating, what you are doing. But you also need to set some realistic intermediate targets, that make it worth your time. I am not talking about being a pro or anything, but if you play as a side hustle, you should probably be able to win at least 200-300$/month, if you live in a poor country and 500-1.000$/month, if you live in a rich country. Otherwise its just not worth your time.
So as the previous poster said, for cash games you need to get to at a minimum 10NL, and this is only, if you live in a poor country. Winning 20-30BI per month at 10NL is realistic for a good part time player. If you live in a rich country, you probably want to reach at least 50NL, if you are going to play cash games for profit, because otherwise its just not worth your time.
As the previous poster said, you can start at 2NL or 5NL, but starting any lower than 10NL is not about "building a bankroll". Its about practicing and proving, that you can beat 2NL and 5NL to reduce the risk, you end up as a losing rather than winning player at 10NL or anything higher than that. If your winrate is negative, then no amount of "bankroll" will protect you from eventually losing it all, if you continue playing, and losing kind of defy the whole idea of playing for profit.
The next question then is, which games are best to play, if you play for profit? And as others have said, you need to try different games to find out, what work best for you. In my experience though it is easier to make money in MTTs than in either cash games or STTs, and the main reason is, you pay less rake per hour, you play. This is especially important, if there is no meaningfull rakeback, as is often the case these days.
However MTTs are a rather complex game form, so I dont recommend starting with them. To become a good MTT player you should probably have played at least 100.000 cash game hands and 1.000 6-45 man SnGs, before you even start to think about playing MTTs. The cash games will teach you postflop play and the SnGs will teach you short stacked play and ICM.
To play MTTs I recommend a bankroll of at least 500$, since this allow you to comfortably play a mix of 2-5$ MTTs, which is wide enough to give you good volume on most
poker sites. I also recommend not doing this on PokerStars, because their rake is higher than anywhere else. I have personally done well in the MTTs on
888 Poker, but I am sure, many other sites can work as well. With MTTs you should be able to have an ROI of maybe 30% for micro and low stakes, and for that reason rake-back and bonuses are not to important.