You want at least 20 full buy-ins. If you start at 20 buy-in's though, be prepared to move down quickly if you start to lose. 25-30 buy-ins is much better.
Keep in mind that at $2NL ($.01/$.02) and $5NL ($.02/$.05) unlocking the bonus will be difficult, as it's hard to collect FPP's. You only get an FPP when the pot reaches $8 or more.
So to be specific with your question:
$400NL ($2/$4) would be at least $8k, but $10k-$12k is much better.
$200NL ($1/$2) would be at least $4k, but $5k-$6k is much better.
$100NL ($.50/$1) would be at least $2k, but $2.5k-$3k is much better.
$50NL ($.25/$.50) would be at least $1k, but $1,250-$1.5k is much better.
$25NL ($.10/$.25) would be about $500.
Anything lower than this I think you can get away from the bankroll management rules a bit as play is weak enough that being a little underollled isn't going to matter as much as the weak play will make up for downswings. Of course, if you're losing you should move down quickly.
Dumpy620_84 is on the right track for his bankroll. $720 is plenty to play $25NL ($.10/$.25).