If you can wrap your head around C/C++ then you'll find picking up most languages to be a breeze. Also, writing some bash scripts to automate some tasks for you is a great way to get your feet wet. Do some research on the following topics. They'll get you in the right mindset to program:
If, then, else statements
OOP ( object oriented programming)
Compiled vs Interpreted
You don't need linux to program, although I use linux for 99% of everything I do on a computer, especially programming. I find the environment easier to work with. Either way, you should still give linux a go. There are many great distros out there and you will probably find one of them very suiting.
"The art of war teaches us to rely not on the likelihood of the enemy's not coming, but on our own readiness to receive him; not on the chance of his not attacking, but rather on the fact that we have made our position unassailable." - Sun Tzu