Everyone has an opinion of how to connect fans. If they are quiet or you do not mind noise, connecting to the power supply will give you full speed at all times.
For me personally, I like to let my boards control fans. Not all boards control all fans well, check your manual for the board.
Looks like you only have 2 extra fan headers on board, you can use 3 pin splitters to connect to the board, but do not over do it(low power fans up to maybe 3 and 2 for most other fans. extremely powerful fans should be run without others). too many fans can damage the board.
Many users also use front bay fan controllers to give manual control over many fans at once.