When should I move up/down earlier?

The standard value for a jump in limit was given as 300 BB in the beginning BR management article.

This value is arbitrary, however, and provides no guarantee that you will not have to move back down.

Suppose I have 300 BB for the $1/$2 limit, that is $600. It is quite possible that I will be confronted with a 100-150BB (200-300 dollars) downswing in my first session and immediately have to move back down in limit.

Since you cannot go back to the microlimits after the 45 days of beginner time, you should build up a bigger bankroll for .5/1 to make yourself very secure on this limit.

I advise every player on $.5/$1 FR to build up a bankroll of $500-600 before going to the next step, like $1/2 FR or $.5/1 shorthanded.