What do you know about the property they will move into?
Size and number of bedrooms etc.
I would start by thinking about how much will go with them - bed/s, sofa, furniture etc. Then what will dress the room, which curtains, rugs, mirrors, pictures.
Then practical things, how much linen, towels, pot and pans, plates etc will they need.
Perhaps some kind of unit or chest to put special keepsakes in.
Once you know roughly what you have on your keep/go list then you need to decide what to do with the rest. Ask the family if anyone wants/can make use of the things.
Anything of value like nice furniture or art can be sold. If its not really worth anything then you can get house clearance companies who will literally come and take the lot.
Also ask if there are any charities who could use the stuff. There is one near me that will take anything in a house from coasters to sofas as they help set homeless people up when they get a house.
Are your parents still able to make these decisions for themselves? If so make sure you take their lead on whats what.
Once you (and your parents) have decided what is to be done with everything, I would make any relevant phone calls - removal company, auction house, house clearer, charity etc and make arrangements with them.
Then make a trip home and do the sorting and packing.
Do you have any family or friends who could help you with this as it will be a big job, and a pretty emotional one. Having a friend with me when I packed up my dads house, and my grandads helped me a lot, because I wasn't so inclined to get hung up on each item I picked up and dawdle over it, when I had a friend there giving up her time.