Backing up my Macbook Pro?

I recently purchased a Macbook Air and sold my Macbook Pro. I'll be giving up my Pro within the next few days, but won't receive my Air for a couple of weeks. I purchased "My Passport" for Mac and manually transferred over documents and pictures. I'll be running the start up software within the next few days and I had a couple questions. When I plug in "My Passport" onto my new air, will I simply go to "Backups" on the hard drive and open iPhoto to recieve all my old photos and videos? And also, if I clear my Mac will everything open fine through my time machine on my new Air? I'm new to this and it is quite confusing!

Carbon Copy Cloner (or similar)

I suggest making a backup clone of your MB start-up drive, but your TimeMachine backup should also allow you to import everything you had on your old system. The nice thing about making a clone of your drive (ideally on a partition of your external drive) is that you can actually boot off of it, which could allow you to reformat the new system's start-up drive and make a custom installation (perhaps eliminating any apps that come pre-installed that you really don't want). Of course you would also need the OS X installer handy (e.g. on a thumbdrive).

The other nice thing about a bootable clone is that you can revert to the clone completely if you ever make a software update that messes everything up for you (incompatibility with critical software you use) and it also provides another way to work if your start-up drive goes bad (less likely with an SDD, like the Air comes with) or boot up from the external drive to run disk utilities on the normal start-up drive that cannot be run when booted from it (also less likely to be an issue on an SDD).

As above

You need a cloning app (I use SuperDuper but there are others) to make a bootable clone of your MBP hard drive onto your portable HD.

When you get your new MBA you can use migration assistant to transfer all the date from your clone onto your new machine.

Migration Assistant will automatically know not to copy over the old system, or applications that it knows will not run, but it will copy over everything else. It's quite intelligent and, when used according to directions, flawless.