As a Holocaust/Genocide Studies educator I have visited Auschwitz-Birkenau 2X. I had much prior knowledge of these camps, but I also learned so much more. I did travel with Holocaust groups. None of us (with various familiarity/knowledge) were prepared for the nearly overwhelming emotional toll the authentic sites inflicted on us. (I have also visited & studied in 3 other death camps in Poland & in numerous Concentration camps.)
That written, I strongly suggest you book a tour from Krakow (one of my favorite Euro cities)..
This would solve your transport, tix, & probably give you a proper tour with info and protection.
I say protection as these 2 camps contain memories, documentation, & evidence of astounding evil.
You say "we", but don't state adults or children. As a long time Holocaust educator experienced in school & in these camps, I implore you not to take any young children or even mid-teens here. Personally, if I had a chance to take my 10-11-12 graders here, I wouldn't.