So I don't have to "back up" applications?
As long as you have the CD, or can get the off of the internet.
You should be doing a clone to an external USB drive as your backup.
A clone in a bit for bit copy of your hard drive and it is bootable.
I think that superduper is the easiest application to use, but other people use carbon copy cloner. They are both free. The clone will contain all the files of your hard drive. You will need a USB drive that is large enough to contain all the the contents of your main drive. Also test out the backup before you upgrade.
To boot off the USB drive hold OPTION while your Mac is booting up. You can then select which drive to boot from.
iPhoto 6.0, iMovie 6.0, Safari 4.1.3, Firefox 3.5.19, Word 2004 (but I have a disc for the latest version that I can install, but not under tiger - hence one of the reasons to upgrade)
Safari will come with Snow Lep & the latest version of firefox can be downloaded for free at their website.
I don't know about the others off hand but if you google "iPhoto 6.0 requirements" you will be able to find them.
Is this an option I should take? What does the clean install DO?
Also, how much RAM, or other requirements do I need? (Again, speak to me in layman's terms).

And where do I go to find out if I have enough? (No tech lingo please...and thanks for your patience to a non-techy person.)
A clean install is basically an erase of the entire hard drive and a fresh install of the OS, then apps & data. All your data will be in your backup. I dont think that you can upgrade Tiger to Snow Lep without having to upgrade to Lep first. You can always do a clean install.
I always do a clean install when I upgrade my OS. It removes any leftover junk.
Note that to do a clean install you need to -
1) Boot from Snow Lep CD
2) Disk Utilities from the top menu
3) Erase the hard drive
4) continue with the install.
If you do not erase the hard drive BEFORE you install then the OS will upgrade the OS & you will not get a clean install.
Also, how much RAM, or other requirements do I need? (Again, speak to me in layman's terms). And where do I go to find out if I have enough? (No tech lingo please...and thanks for your patience to a non-techy person.)
To check on your Mac click on the apple in the top left -> about this mac.
Snow Lep System Requirements
http://store.apple.com/us/product/MC573Z/A
Mac computer with an Intel processor
1GB of memory
5GB of available disk space
DVD drive for installation
Some features require a compatible Internet service provider; fees may apply.
Some features require Apple's MobileMe service; fees and terms apply.