Help with oyster?

Hello, I am still confused with the travel options in central London and the best value weighed against restrictions (for example only travel after peak). I will be staying near the London aquarium, my child can travel for free, on-line ticket purchase and free child entrance to sights is better value in all circumstances except 2-4-1 London aquarium and 2-4-1 Lego Windsor. Most sights we will visit are in zones 1-2 except Kew Gardens, Lego Windsor, and Hampton Court. ( I have created a separate thread about the last two and possibly staying in Feltham.) I would like the flexibility to travel during peak and gain early admittance to some sights before crowds. It is too close to my departure date to have a visitor oyster card mailed to my home. I will not have a car seat for my child so taxis are not an option I have read. I have also read that the buses will no longer accept cash fares.
I think an oyster card, with a 7 day travel pass for zones 1-2 is the best option and this will work for me on the tube and buses with my child traveling for free. Does this sound correct or am I muddled in my thinking? Thank you.