You could also consider renting an appartment, right in the old town. Try sodispar.com, you pay when you arrive, and if you've a mobile they'll meet you outside the appt. Try bargaining if going off-peak.
There's tours to Auschwitz from about €20 & there's people handing out leaflets on the street, so you'll get info easily enough. I found Birkenau even more horrific than Auschwitz.
If you want to see some classy Communist architecture, i'd recommend Nowa Huta (#4 tram to last stop Parc Centralny). I think it'd be worth doing a tour of it (but only after you've seen Auschwitz/ salt mines / jewish quarter etc) , you may be able to get a visit into 1 or 2 appartments.
It has a big steel mill which at one stage employed 70,000 people.
There's a tram/train that goes right from the airport into city centre, runs every 20 to 30 minutes.