I'm looking at http://www.codeblocks.org/downloads/26 and I'm not sure which version to pick?
I'm guessing I should either use
codeblocks_16.01_amd64_jessie.tar.xz
or
codeblocks_16.01_amd64_stretch.tar.xz
since I'm using a 64 bit amd processor.
I've only recently started using linux more often, so I wasn't bothered by the fact that the software manager on linux mint only offers C::B 13.12.
Also since I'm only used to installing from the software manager I'd probably need instructions on how to install it?
IIRC, Linux Mint uses dpkg/aptitude as its package manager. For such a widely used distribution, there's probably a package available.
Try issuing (at a shell) $ sudo su -c 'apt-get install codeblocks=16.0.1'
Edit: I didn't read the question fully.
You probably want the stable version (for Debian Jessie) of the package.