You've raised two basic question
pinkn
1. Can you use your BA miles to fly other airlines in the alliance?
The answer is "Yes"
How you do it is subject to the rules of the BA frequent flyer programme - see
this link to start
2. What is the best way to accrue miles when flying various airlines in the alliance?
The best way is to chose which one airline's frequent flyer programme best suits you and accrue all your miles to it (by entering your ff number for that programme into all your bookings).
Which airline is best for you will depend on your flying pattern and what you want to do with the miles you accrue (redemption flights, upgrades, shopping,...)
This thread might help