Train from KIX to Osaka or Umeda

Hello. I am arriving at KIX around 8:30pm. I need to get to Osaka or Umeda station. Can you tell me the best way to get there considering:
1. I don't want to take a taxi. Too expensive.
2. There are 6 of us. 4 adults and 2 kids.
3. Speed is important but so is cost.
4. If if get the Kansai Thru Pass, will this work then use it the days after?

Your inputs are most appreciated.

Thanks so much.

I recommend taking the direct JR Airport Rapid trains for speed and convenience. I think you could do it more cheaply by Nankai and Midosuji Subway Line via Namba, but the transfer at Namba is not very convenient:
http://www.japan-guide.com/e/e2033.html

4. If if get the Kansai Thru Pass, will this work then use it the days after?

The Kansai Thru Pass does not cover JR trains, but it covers Nankai and the subways. It exists as 2-day and 3-day pass. The days do not need to be consecutive days:
http://www.japan-guide.com/e/e2357_005.html

To go direct from KIX to Osaka station, you have trains and buses. See, resoectively, Hyperdia and the access page of the airport's website. Since the trains are with JR, they are not covered by the KTP, if you want to be covered by it, you will need transfers.