Downsizing my Mac

My present MacBook I was able to upgrade to 1 TB but the cost of buying the new one with this amount of storage may be more than I am willing to pay. Should I reduce the storage on my present MacBook (650 GB at present) by off loading less frequently used data onto a separate hard disc or can this be done with the backup after my present Mac fails?
What happens if I try to restore a backup onto a new Mac with less capacity than the backup?