birth control after having baby?

sooo ive heard you're like SUUPER fertile after having a baby.. I have a couple years of school to finish and it's already going to be hard enough with one kid.. I dont want another right after... but I always hear stories about people not being able to get pregnant for a really long time after getting off birth control.. I dont want to have to wait forever and ever once im ready again.. so is the having trouble getting pregnant super common? is there certain birth control that doesn't cause this problem?? 🤔