Polish, Czech, Slav... similarities?

Good evening.

Purely as a hobby, i've decided that i'd like to pick up a European language (I already speak a couple Asian languages).
I initially wanted to learn Czech, but i was comparing populations that speak languages in Europe and found that Polish outnumbers it and that it also has a lot in common with slavic languages.

tl;dr:  Anyone who speaks Polish or Czech, or any combination of those Slav languages, are there similarities?  'ppreciate your comments.

You West Slavs must recapture Carantania!

Emigrate from your countries and settle in Vienna, establish your business enterprises, beget as many children as possible, teach your children the Pan-West-Slavism, choose Slavs for local assembly then the Austrian national assembly, choose a Slav for the Austrian President, change the name of the country from Austria to Catarania, change the national language to a Slavic language, and finally unite the West Slavic countries (i.e. Poland, the Sorbian autonomous regions in Germany, Czech Rep., Slovakia, Catarania, Slovenia, Croatia) to connect the Baltic and Adriatic!
How many centuries might it take, you Slavs must go for it!