Does paying the statement keep progress even if I spend it?

I just got my first credit card and my statement balance for last month is paid, I’m getting the new statement maybe on Monday. Im confused bc it’s my first time having “bills” (im 23).

So if my statement is $600 and I pay it, does that fulfill the statement? If I spend the $600 does that erase it and go back to 0 and I owe $600 again? What if my balance is $1000 but I pay $700, does it give a $700 progress and stay there regardless if I spend?

Whenever I get paid, should I put the money on the credit card and spend it there? Or should I use the credit card and then use my debit to pay the credit I just used?