Linux is not Windows. Stuff, including drivers, is not installed in the same way. This article from Ubuntu
provides a pretty good overview.
In my experience, HP provides the best Linux support. My HP OfficeJet Pro L7680 has worked flawlessly with almost every distro I've used (Mageia 3 had some problems with it, but they were resolved in Mageia 4.)
If you go HP, you want to make sure that HPLIP
is installed on your system. It's in most distros' repos and can be installed from the package manager. Note that, in many cases, the HPLIP GUI is a separate package from the HPLIP base and must therefor be installed separately.
By the way, Mint 15 has reached end of life
and is no longer supported. V. 17 will be supported until 2019--I have it on a computer and it's working just fine. You may want to look at upgrading.