The USB Thumb Drive boot method will work fine. I don't know what they have against it, but I'd be shocked if you didn't have positive results using it. As a matter of fact, any apt-based Linux variant that uses a filesystem structure similar to Ubuntu will work fine. That includes Debian, Mint, and others.
Anyway,
to download Ubuntu, I prefer using a torrent. It reduces load on the servers, it's faster, and the integrity is verified as you download.
For people brand new to Linux, while Ubuntu is easy,
Mint is easier, better looking, and more "familiar" all around. You can
download a torrent for Mint as well.
Once these downloads finish, you may burn them to a CD using a free CD burning program (on Windows, I like
CD Burner XP) - 5mb freeware without bloat, and burns files with ease.
If you want to install it to a USB drive, back up the contents of the drive first, and use
Universal USB Installer to get the job done. The program is simple to use. Pick the ISO file, tell it where to install to, and tell it to do the job.
The only hiccup you might run into is if your computer is old, you may be told that your CPU doesn't support PAE (Physical Address Extension), which allows it to access memory in a different way than older CPUs (oversimplification). If that happens, you may try Xubuntu.
To boot the CD or the DVD, you will need to go into your computer's BIOS settings (F2, F8, F12, or ESC immediately when you start the computer, usually).
Once inside BIOS, you're looking for "boot priority", or something similar. Use the toggles to change the order to something like:
USB Hard Drive
CD/DVD ROM
Internal Hard Drive
Floppy Disk
Common toggles are page up/page down, plus/minus, and spacebar.
What these settings will do is cause your computer to look for a boot partition on the USB Hard Drive - if it finds one, it boots it. If it doesn't it moves onto the CD/DVD ROM and does the same thing. If nothing is found, it boots the internal hard drive. This all happens in less than 2 seconds, so it's safe and advisable to leave the settings like that once you've set it up that way.