If you use Migration Assistant (I can highly recommend it), what you do is follow along with the welcome screens on the new computer and then it will ask you if you have data you want to migrate over. Then it asks you to choose a source. One possible source is a Time Machine backup (which you choose on the screen and then it tells you to plug it in after that). Another is the actual other computer (again, if you choose that radio button and it tells you to connect that old computer to your new one). If the data you have is the same on your TM backup and on your old computer, and your old computer is not physically broken, I'm not sure there's a compelling reason to choose one over the other. They should both work.
Here is the thing on the usernames:
When you go to migrate your old computer and it's user name(s), well, the way the Mac works is there can't be two of the same user name. So if you ALREADY had started up your new computer, skipped the migration, made your (same) user name and played with the computer, and THEN tried to migrate, well the migration would go "Oh, there is already a DanMan" (or whatever the name was). So it would make your whole new username with all your new migrated data "DanMan1"
For that reason, it's good not to start up the new computer and get it all personalized with "DanMan" and THEN migrate. Because you will have an empty "DanMan" account, and a "DanMan1" with all of your data and everything. And the Mac is a bit skeevy about changing your short name.
Some people fire up the new computer and play with it with another ("throwaway") user name, then migrate their real username and make it the main one (and that will work). I just once read that certain hidden things are attached to the first main username, and I don't know if it's true or not, but I figured it does not hurt to play it safe. You can also "fix" it later by going in, renaming the first "DanMan" to something else, then making "DanMan1" into "DanMan, but again I think that might mess with hidden short name stuff - not sure though.
On my new MBP, I wanted to fire it up and make sure it worked okay and screen was good, etc., so I played with it for a while and then put in the system disks and did a fresh install, and then migrated. But this fit my grand plan as I did not want iLife 11 and instead wanted to keep my iLife 08 from my other computer. So I just did not reinstall iLife and then ILife 08 came over from my old computer.
If I had not had that plan, I probably would just have migrated over when I first started it up. After all, if it proves defective, you can THEN wipe it out, reinstall the OS and return it to Apple. Chances are that won't be necessary. That's what I did on my 2008 Macbook and it worked just great. Just turn it on, follow screens, use Migration Assitant, and away you go!
I also make a second administrator account (later, after all migrating is done), just in case I ever need one.
Some people don't like to use their main (root) account for daily use. I do, but there may be something I don't understand and maybe that's not the best (?).
At any rate, I do know that what I said about user names is correct, and that if you have DanMan on the computer already and then go to migrate you will end up with a bit of mess to fix.
I have had great luck with just firing up, using Migration Assistant to move everything over, and going from there. But then I never had a dangerously, horribly, scarily messed up computer, just an old sloooow one.
