External hard drive to work with Windows, OSX & Linux?
Solution 1:
Does the Mac absolutely need a GUID to boot up from the external hard drive?
Yes. Apple has a support article on that.
Let's say I want to try a new Linux distribution, I put it on the external hard drive, does it have to be on GUID partition in order to show up and boot up on the Mac?
I would think so, yes. You might need rEFIt for that though. But even then, they say that "booting Windows or Linux from an external disk is not well-supported by Apple’s firmware. It may work for you, but if it does not work, there is nothing rEFIt can do about it."
What type of partition does Time Machine need in order to work? Also, will it work if the external hard drive has more than one partition?
It has to be an HFS+ Journaled partition. And yes, it works if you have multiple partitions. You can just choose which partition to back up to once you plug in the drive.
How do you recommend I partition the hard drive so that everyone can use it and I can boot up from it (OSX/Windows/Linux distros) and I can also use it for Time Machine?
You definitely need a GUID partition table and a HFS partition for the Time Machine backup. That leaves two choices for data partitions:
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Linux has rather good NTFS drivers these days, so you could make your data partition NTFS. Unless you need to access it from your Mac. In that case you'd need the NTFS-3G third party driver, which works quite well for me though (install through Homebrew for example).
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Windows and OS X fully support exFAT. Linux however doesn't, so you'd need a third party driver again.