My iMac backs up to an external hard disk - which is now full. It is erasing the first backups of course to make room.

I now have a new external hard disk. As this one is larger, I wondered if it might be better to use the new one instead of the older one and use the older one for other data.

How do I go about that please? Can I move Time Machine to the new drive, wait until it has a week or so of backups and then erase the old drive? Will Time Machine complain about the change?

Both the iMac disk and the old drive are about 300Gb, whereas the new one is 1Tb. Which is the best one to use for Time Machine?