I cant answer all your questions, so Ill start with welcome to Coffee Snobs.
Re tamper size - GO to the Pullman Tampers website (link on the left) and there youll find info on the difference a good fitting tamper can make.
Start with a level basket full of coffee and see what you think. It really is about finding the right grind size, amount of coffee and possibly other variables, that work for your particular machine.
Try Coffee Parts or DiBartoli for the knock box - see the links on the side.
Now some qustions from me.
Have you got a good grinder yet?
Im going to assume no because you want to use the pre-ground Illy rather than freshly roasted beans.
Do you realise pre-ground coffee is stale?
Have you tasted freshly ground freshly roasted coffee?
What coffee were you using commercially?
What makes you think the machine is warm in under 60 seconds?
This is the start of a loooong journey. Have fun.