I need to do a full backup of a Mac running Tiger. If I use Time Machine will it capture everything I need to restore a user's data after a clean install of Lion? Are there other better mechanisms I can use to perform the backup?
You have two main options. Depending on what you want exactly and how much of your current user information/settings you want to migrate.
This is the method I prefer. i believe that when doing a clean install the point is to get rid of all the extra junk that is just sitting on your computer. To do this you need to manually backup your stuff data. Just go through all your folders and copy the stuff to an external HD. (Desktop, Documents, Downloads, Movies, Music, Pictures, Public, Sites, Bookmarks, Adress Book, Mail, etc). You leave all your settings/preferences behind. This makes for a real clean install.
Using backup utility
I would suggest using CarbonCopyCloner. It's free and works on Tiger. With this clone your current hard drive and after doing a clean install Lion will ask you if you want to import your stuff from a previous installation and you can select the clone you just made. Keep in mind that this will also copy back all the preferences/settings and junk you might have accumulated. Thus in my perspective defeating the point of a clean install.
This is probably the best option. Make a clone with CCC and then instead of having Lion automatically bring back your data, do it yourself manually. This way you will have everything saved from the clone and you will be able to bring back only the important data you want and not any overhead.
Do you need to do incremental backups, or just make one perfect backup, such as for transferring to a new machine?
If you just need to do the full backup, you can use CarbonCopyCloner. That will make a full byte for byte backup (that's even bootable) onto another machine. You can then copy over user files (such as Music, Movies, etc) to the new machine once the upgrade to Lion is complete.
Now, normally I'd suggest using Apple's Migration Wizard, the built in tool to transfer files to a new install. But since you have Tiger, the migration wizard will not work. So your best bet is to copy over files manually. You may want to only copy over user document folders (Music, Movies, etc) and not Applications and ~/Library as it's likely you'll run into some issues going from Tiger to Lion. Install fresh apps, copy user data, and recreate everything else.
Time Machine was not introduced until Leopard, so you will not be able to take a Time Machine backup of it, unless you were able to somehow connect the drive to another Leopard-or-newer Mac and back it up that way. Perhaps by Firewire target mode, depending on what you have access to. I cannot say what is best to use as I never owned Tiger for more than a few weeks, but TM is out of the question unless you fudge it somehow.
An alternative to Carbon Copy Cloner is SuperDuper! I used CCC for years but moved to SuperDuper! for its ease of use and cleaner design.
The idea of having a bootable copy of your computer, updated daily (SD does smart backups) is important. If anything happens to my computer I can either boot any Intel Mac (I use GUID partitioning) from my backup or get another computer, start up from my backup, run SuperDuper!, erase the new hard disk and copy the backup over to it.
While I do use Time Machine I still find SuperDuper! the better backup tool and it takes about 15 minutes to copy my 500GB SSD to a 500GB 7200 RPM rugged drive with firewire 800. I do it daily while cooking dinner. Easy.
Oh, and because we heat our house with wood and so run a higher risk than many of a house fire, I have two backup drives, one in a fireproof case in the basement, one in my desk. I swap them daily. I've been backing up like this for over 10 years with CCC or SD.