Please notice that "Unix" is not an operating system - not in the sense of "Windows is an OS" or "Palm OS is an OS". Its an architecture, a design blueprint for building actual OSes. "Unix" specifies that there have to be certain features, certain interfaces, certain ways things work, etc.. In a narrower sense "Unix" describes the way the OS kernel works.
Depending on what you want to learn you will probably not be affected by the difference between "Linux" and "Unix", because (you said you are a beginner) the two work identically viewed from the outside. The differences are rather esoteric points in the kernel design, which will most likely not affect you at all.
Using different Unix flavours is a lot like driving different car models: yes, its different somehow, but basically a steering wheel is a steering wheel, a brake is a brake, the gear shift is similar to the gear shift in the other model, etc..
Many Unix dialects are not free at all and will either only run on very specific hardware (like AIX, which only runs on IBMs p-Series) and/or cost money.
The bottom line is: download a Linux distribution of your liking and as long as you don't have to learn some very very specific details about OS architecture you could use the terms "Unix" and "Linux" interchangeably, because any Unix will more or less work like Linux and vice versa.
You might be interested in reading the
Rosetta Stone of Unix for some of the more obvious differences among the popular flavours of Unix.
I hope this helps.
bakunin