I was in Poland a couple of years ago when Czech president Havel visited. He used an interpreter. Poles say that Czech sounds like "baby talk" to them. Slovak is closer to Polish than Czech is.
"Mowimy po Polsku" is a good introduction and has audio tapes - published in Warsaw but available in this country. "First Year Polish" by Oscar Swan (Slavika Publishers) is published in the US and is good. Hugo's "Polish in 3 Months," is a good introduction.
I've been studying Polish and going to Warsaw since 1999 and still make a lot of mistakes, but the Poles really appreciate your learning their language and are very encouraging and helpful.
It's a great country with a great people.
I've worked a number of assignments in Belgium and Germany for NATO. It would be a pleasure to assist a relocation of the German assets to Poland. Your comment about Poles perceiving Czech as "baby talk" was also shared with me by Polish support engineer in Reston, VA. He was scheduled to do a software installation at a Czech business. Polish will be another linguistic stretch. I've mastered enough French, German, Turkish and Welsh to operate comfortably in those languages. I've only dabbled in enough Japanese to conduct Judo and Aikido tournaments.