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There is a Linux mint forum zeo. I joined the fedora forum a couple years ago.
Just type in Linux mint forum in your browser.

The advice Molly gives is a good one. Sign up for the LM forum, generally very helpful there.

I run an old laptop, currently with Mint 17 Mate DE, for 'try-out' purposes and while I think a two-week user is not in the best place to start messing with old packages, this for information.

1. You might be able to use the dumbed-down Mint software manager but you might need Synaptic package manager, which is a bit more hands-on. Most linux's default to the latest version so you do need adjustments.

A bit about versions. Mint 17 is based on Ubuntu 14.04 'Trusty' That Gimp-Painter package is aimed at Ubuntu 12.04 'Precise'

2. First thing is check that the ppa points to precise.

If you find it in the packages list, it is possible to edit (do the painter-sources as well).
looks like this: http://i.imgur.com/CfGEGSP.jpg

3. Providing that is ok and the sources have been refreshed/updated.
Where to find it?
Look for Gimp. Right click. Click on Properties then Versions.
looks like this. http://i.imgur.com/vHHvKhL.jpg

Am I going to try an install? Not a chance. Very likely to break something.
At a guess, you will need to do the same 'force-version' for the packages gimp-data and libgimp2 as a minimum.

IMHO a better way if you are not bothered about latest-and-greatest is install Mint 13 which is based on 'Precise' Even better, free up some disk space and install it to dual boot with Mint 17.

Rich is right, Gimp Painter 2.6 was created during the Ubuntu 12.04 release, so trying to install it on a more recent version of Mint could quite likely break something. The instructions below should show you the way if you're willing to take the risk:

http://www.ramonmiranda.com/2012/02/whats-gimp-painter-part-2-installation.html

Note that it shows 2 methods, 1st method involves removing your standard Gimp in place of Painter 2.6. Second method involves installing it manually and separately. I'd say the second method sound better, but I can't guarantee anything. Its a big risk if you decide on going ahead, mind.

You could try it out from your Mints live CD first if it allows it - that would be the best approach.

Alternatively, I could try to cook up a Puppy Linux ISO with Gimp Painter 2.6 pre-installed. Puppy is a portable distro that works with a savefile, so you don't need to install it over your current OS. Would need to know if you have a 32-bit or 64-bit system.

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Not Gimp 2.10 I think that might still be a little way off, but Gimp 2.9.1 from a ppa will be easier to install than Gimp 2.6 in Mint 17.

As of last week the mypaint brush engine appeared, looks like this in my Mint 17 You can see I am no artist but find a bit of doodling relaxing