I just bought a portable hard disk and want to allocate 10 to 20 GB of it to linux while having the rest of it be a storage partition (NTFS)

For linux there are two different options I can see. I can make a 'persistent live' install or I can attempt to install linux normally.

I am aiming for maximum portability, so I want to be guaranteed that the install can be ported to machines with completely different hardware configurations and not break, so I'm kind of leaning towards a persistent live install.

Or can a normal install be made to be portable?

Candidate OSed i'm thinking of using are Zeven OS Neptune, Pinguy OS, or Linux Mint.

Personally I prefer a normal install just as if it were a real internal hard drive over the usb flash type installs.

Regular installs offer a better way to update and install apps.
Flash drive installs offer smaller space and maybe in some cases a bit faster.

In most modern linux distros (other than specialty distro) all can be installed to usb drives.

I'd remove the internal drive before you attempt this. Then install from cd/dvd as normal.

Portability may also be limited by unique drivers. Most desktops are well supported.

Some odd issues with grub and grub2 but that can be fixed.

Might need to set a /boot partition low in the scheme.

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