It really depends on your understanding of the game, how much you can lose without it effecting everyday life, and what you are are trying to accomplish (Have fun, make extra income, make a full time income, ect.). If your new to the game, don't have a lot of extra money, and you're just trying to have a little fun deposit the min, and play micros.
Now on the other side of the spectrum. If you have Played a lot, know the game, are taking it seriously, and trying to go pro. You are gonna need enough bankroll to cover variance at the very least 1/2 cash. So about 20K....
In other words, it really comes down to how much can you lose and still pay your bills. Along with how seriously do you plan on taking it.