Tell us more.
Are you buying a new Mac?
How old is the old one?
What version of the OS is on it?
A tm backup will work well enough.
Basic instructions:
Just before the new Mac comes, run tm "for the last time" on the old Mac.
When the new one comes, take it out of the box and put it on the table.
DO NOT open the lid yet (if it's a MBP) or press the power-on button.
CONNECT YOUR TM (or other) BACKUP.
NOW open the lid for the very first time -- the MacBook will boot automatically when you open it (you don't press the power on button anymore).
Begin setup.
At the appropriate moment, setup assistant will ask if you wish to migrate from another drive. YES, you do.
So... "point the way" for setup assistant to find the tm backup.
Give setup assistant time to "digest" what's on it --- it can take a while.
Setup assistant will present you with a list of stuff to migrate.
I suggest you just migrate it all --- EXCEPT, if your previous Mac is pretty old, you might want to skip migrating applications, and just install them "fresh".
If it's relatively newer, most of the apps will probably be working.
This is up to you.
Let setup assistant do its work.
Again, it will take some time.
When done, you should see your old login screen just as before.
So... log in and "look around".
Good luck.