Such good advice above. It's one of the hardest things I think, physically, emotionally and in terms of dealing with finances, legalities, logistics. Do really make sure you give yourself enough time (although having a firm deadline does also focus the mind) and don't make life unnecessarily difficult practically e.g. hire a skip if needed rather than doing multiple car trips back and forward to the tip.
Totally agree re absent relatives and siblings sometimes being the hardest thing to manage, you do need to set firm boundaries e.g. if they want sentimental items kept they need to collect and store them themselves within a reasonable timeframe or put up with the fact they'll be sold or dumped - you don't need to say it as brutally as that, but I've found myself being used as an indefinite storage facility for bulky items e.g. a damaged piano, a heavy display cabinet, a non working grandfather clock that various people in the family were so attached too they kicked up a huge stink about them being disposed of but 'didn't have space for right now' don't want in their house or 'haven't got time at the moment to come and get' will never come and get . I'd set a relatively tight timeframe for all relatives to visit the house and take any sentimental items they want (obviously first remove anything particularly valuable or specifically left to someone in the will) and after that everything goes, no ifs no buts.
Also totally agree that you (and relatives/siblings) need to let go of the idea that a lot of the stuff in the house is valuable. It's hard (even aside from the sentimental issues) because some things in the house probably could be worth something but the time and effort involved in listing things on eBay or car booting or whatever will likely not be a good return on investment. I would certainly either get an auctioneers house in to quote for house clearance (as per pp they.will charge for their labour in removing and sorting through everything, then a % commission fee on anything they can sell) or get British Heart Foundation or another charity to remove any furniture they can sell (try not to be hurt/upset if there are good quality items they can't or won't take, some things like sofas have to have fire tags, some things that are old fashioned just won't sell). You probably are going to have to somewhat lower your own standards re recycling/reusing absolutely everything as you would if it was your own home.
In terms of approach, personally I've found sorting via item rather than by room the best approach. So first I gather all obviously valuable items and important paperwork, and put aside/take somewhere safe. Then gather and sort all other paperwork. Then all clothes, then all books, then all kitchen items etc. Doing it this way also helps if you have people coming in to take items for themselves and you can also then delegate certain jobs to others e.g. right sister you're in charge of clothes, brother you're on garden stuff and plants, DH you're emptying the garage etc. As you go I do find it gets easier to be brutal and let stuff go particularly if you've started with the harder items and move on to easier. The Marie Kondo technique of taking photos of things you are going to get rid of helps, and even the slightly cheesy thing of holding the item for a second, 'thanking it for it's service', then saying goodbye. One thing I would say not to do, although tempting, is don't put stuff into storage or bring it back to your own house to be sorted at a later date or without a clear plan of action for its future - my experience is this stuff will just then fester forever like a non healing wound. Of course choose and keep some keepsakes but I think emotionally it's important to put these things into their permanent place in your home then let go of the rest, maybe I attach undue importance to possessions and material objects but while a person's 'stuff' is still in transit I can't help feeling the person themselves is still in flux and I can't really move on in grief. Obviously it does mean an intense period of sorting and disposing of stuff and being prepared to take a risk that you'll bin something you later wish you'd kept but actually 99% of the time it's the other way, you end up saddled with things you really could have gotten rid of. The only exception is paperwork where it's worth being a bit cautious and holding on to things which could be useful for probate until that's gone through.
Good luck!