This size is determined by the number of inputs and outputs that were used/generated by your transaction. It does not matter if you used 10 10BTC inputs, or 10 0.00001 BTC inputs, on average, the size will be the same because 10 inputs were used (on average, and when you have the same amount of outputs).
This being said: I often try to cheap out on the fees when i transfer funds between my own wallets... When sending to a thirth party, i usually use a little more than the recommended fee of https://bitcoinfees.21.co
Wasn't aware of this so thanks for posting it again and for sharing fee site.
What I would like to know now is how can I know the size of the transaction am going to generate when sending BTC from my wallet.
Some wallets help with this (Bitcoin Core + forks of Core, Armory), others do not. You just need to use the right software.
I use Electrum: do you know if it's possible with it?