Many people find this the hardest part of the whole process. These personal bits and pieces evoke so strongly the presence of the deceased that it seems almost blasphemous to move them from the very place where the deceased last put them.
That apart, deciding who gets what can be very fraught: it can split families for years to come. So it needs handling with kid gloves and oceans of tact.
If you are lucky, the deceased will have left a list - possibly in the Will; possibly somewhere else - indicating his/her wishes about who should inherit the most valued or valuable possessions.. It is worth looking for such a list; even waiting for a few days for it to turn up.
Without it, you are in a difficult position. In some families, the choice is to get all the closest relatives together and present them with a list of all the possessions likely to be of any interest (this could include furniture if the house is now unoccupied.) Then each person is given the chance to claim an item, probably starting with the most senior (but some start with the most junior.) This process goes on until everything has been claimed. It does not lead to a perfectly equitable distribution, but it is open, transparent and defensible. It does, however, depend on getting everyone together, and these days that is hard. (They will all have made a big effort to get to the funeral: they will be reluctant to foregather again.) Some people try to adapt the same principle and administer it by post,, email or social media; but if the list of possessions is at all long, this can drag on for ages and just increases the stress.
Doing it by Zoom may be possible. We know of no such arrangement having taken place, but it is not difficult technically and if you can get everyone to join in, it may be a way forward.
If there are few close family, a senior member may be ready to act as honest broker, perhaps having taken the trouble to talk to everyone concerned before making a distribution. “I really want those two big decanters they bought in Prague. But Sheila likes them too. Pity to split them up. We can toss for them if you like…” Sometimes hard choices do have to be made - there’s only one Cartier watch, after all - and the toss of a coin, supplemented by compensation with other attractive goods - may be the least controversial solution. It is worth taking a lot of trouble to avoid anyone feeling hard done by or cheated. Patience, discussion, explanation, all in outsize portions, can help. The sad truth is that these occasions can bring out the worst in some people; especially if there were unacknowledged tensions in the family before the death.
There will be almost certainly a residue of “stuff” that must be disposed of outside the family. Clothes is the most obvious example but there could be a welter of more durable materials as well. Charity shops are the ideal destination, but not local ones. It is worth a fifty mile drive to ensure that Mother’s coat is not observed walking down the street on someone else’s back.
A word of emotional warning. Finally dumping “stuff” at the charity stop can be a wrenching experience. It would be nice to be thanked for all this stuff with its memories and associations. You seldom will be. Charity shop staff, themselves usually volunteers, are working flat out receiving, sorting, pricing, displaying stuff. What you bring has no emotional load for them: it is just more hard work. Be steeled for efficiency rather than compassion.