So now I set faucetbox to send me BTC only if it reaches 0.2 BTC...
0.2 is probably much too high - you will virtually wait forever to get a payout.
0.01 might be reasonable, I think it would result in less than 1% fees for most cases.
The recommended fee is about 0.0001 BTC per kbyte of transaction data. One kbyte will normally be enough to handle a number of those small inputs, so for sending anything from 0.01 to maybe 0.15 BTC your fee would be 0.0001.
Onkel Paul