there are plenty of guides to bankroll management, most of them suggest you have 30 buyins for the level you want to play, so in order to play 2c/5c you should have 150$, for 5c/10c you must have 300$. anything under 150$ you should be playing 2nl or 1c/2c. good luck.
You have it dead on. 30 buyins is an average level, but a lot of bankroll nits suggest 50. The absolute lowest I would ever suggest would be 20 buyins, but I would never do that myself. I move up when I am at 30 buyins and if I lose 3 buyins at that level and drop down to 27, then I go down a limit and build it back up and reflect. The bankroll nits like to have that extra cushion not only for safety, but also in case they see a really juicy game that is a limit above what they're playing normally, because they will then be rolled for it.
Seems like a lot of people in the thread are new(er) and don't have much of a concept of BRM. The reason we employ bankroll management is because it doesn't matter how good of a player you are, you are going to have your downswings, and variance will come and kick you in the ass every once in a while, and if you are sitting at a table with your entire roll, or a good portion of it, and that one bad hand, or string of bad hands come, then bye bye roll. You have no control over it. It always cracks me up when I see posts with someone saying that they can play beyond their bankroll because they are really good, but that doesn't matter. Phil Ivey runs into variance just like every other player, it's going to happen.
OP, you should definitely wait until you have $150 before you move up, that will give you some room to work with when you have your coolers without downing your entire roll. I know it isn't as much fun winning a .20c pot as it is to win a $20 pot, but you will get there if you stick to your BRM and learn more at the lower levels. My current roll is at about $2000 and I built that up from nada and stuck to a really strict BRM, so I know it's possible.