Just keep byte variables for each shift register, modify the bits in the variables then shift all of them out.
If you are not conformable with bit wise operations try the bitSet() and bitClear() functions they might be easer to get your head round.
I don`t have to push any button, and I get this.
It looks like the data is essentially random, you should get all 1s or 0s. Are you sure the SR is connected correctly?
Have you got pull up resistors on the push button inputs to the shift register?http://www.thebox.myzen.co.uk/Tutorial/Inputs.html