Some basic info on communication. The wikipedia page has a lot of info.
The most important parts are that it has a redundant pair of 8GB flash drives and they actually upgraded the code in-flight to use both transmitters at once and nearly double the data rate.
I'm not sure how priorities are arranged but it's all going to be sent back relatively quickly in terms of mission lifetime, and I think they managed storage use mostly by putting in plenty.
It was anticipated this would be possible, depending on how the energy budget for the whole craft worked out.