Thanks everyone - it looks like you've answered my question, and I'll mark it as such.
I think that my confusion is related to the mac terminology that you guys are using that I am not familiar with yet - I'm brand new to the world of Apple and Macs, so I've got a lot to learn ahead of me.
"S.U.", you said "The 12.5 mm drives will fit in all unibody MBP's". What is a "unibody" MacBook Pro? The one I have is the aluminum shell, not the older black or white case that appears to be some sort of plastic.
In another thread, you mentioned that you have 2 drives in your MacBook Pro. Is there really room for more than a single drive inside, or did you have to remove the optical drive and put the second drive in its place?
"eww", you mentioned "And it doesn't affect the computer's warranty". When I talked with Apple support about replacing the drive, they said that there are no user-serviceable parts in a MacBook Pro, and it might void my warranty to replace the hard drive. I pointed out that they have several documents at the "Manuals" section of their website, explaining the exact steps to replace the hard drive (as well as memory and battery too), with no mention of voiding the warranty.
Is Apple support always so out of touch with their own web site and their own equipment/policies, or are they usually quite knowledgeable and helpful? I'd like to think that I can count on them when I have questions harder than "where's the ON button". But to their credit, they did mention that I visit these forums to see if anyone here could help.
"OrangeMarlin", you mentioned cloning the old drive first, and I plan to do that. The MacBook Pro is brand new, and has not been used yet, so there is no user data to be lost yet, but it would still be easier to clone the drive than try to install from scratch and hope that everything gets installed the same way as the factory drive came packed with.
While on the topic of cloning the drive and backups, I have plenty of external drives to do backups onto, but how do I go about doing backups/cloning? I've heard of "time machine", but it looks like I need a whole dedicated hardware system of some sort in order to use it? Or can I use it with any external hard drives? Or is there a better/preferable backup tool to use, and does it come with the mac, or must I get it separately?