I took the DIY approach. There was no problem buying a ticket to the camp/memorial online. That should be done well in advance. I can't say how far in advance, because my trip was in 2018. When I rolled up into Krakow, there were some very disappointed people at the tourist office, because tickets were sold out for the next 8 days. Obviously, you'd need to buy earlier than that now.
As far as I know there is nothing special about the tickets a package tour will provide. All pre-purchased tickets allow you to skip the ticket-buying line. That line tends to be long, and it is outdoors, open to the weather. There's no guarantee standing in that line will result in a ticket, so it's important to have a ticket in your hand before you show up at the camp.
All visitors to the camp are taken on a tour by a camp-provided guide, not by a tour-company guide. Transportation is provided between the two camps.
One thing you get by paying extra money for a tour from Krakow is the simplicity of having bus transportation provided. I'd hope the tour company provides a guide to provided background information on the drive to the camp, but I don't know for sure that it does.