Unix is somewhat like a specifications for Open Source and proprietary. Although, one can call -BSD kernels as Unix only and BSD kernels are freely available. Linux on the other hand, is an Open Source Kernel designed for Open Source Unix clone, GNU/Linux.
Regarding which Linux you should use, you have to decide yourself. Tons of Linux distros are freely available to download/install. Basic difference between Linux distros is in Package Management, Graphical Interface ( Desktop Environments, tweaks ) and a few other things. Basic commands are same in all distros. I would suggest you try LiveCDs of as many distros as you can and pick one you like the most.