PurplePeas wrote:
Select Start new or claim existing backup ?
The answer depends on how much you would (or would not) rely on Time Machine's archiving capability.
As you probably realize, Time Machine creates and stores backups for quite a period of time. You may, if you wish, go back quite far in time to retrieve information.
If you choose "Claim existing backup", that period you can go back will stay as it had been.
If you choose "Start New", it will be much more difficult, if not impossible, to retrieve old information. The reward you may achieve, however, is additional disk storage on the device holding your Time Machine backups. (Achieving this reward may involve a manual cleanup on your part.)