I had the same problem when my parents died. They were depression era kids ... i.e., hoarders. Threw away more junk than you can imagine. My dad had put 3 old non-functioning lawnmowers in the attic for God's sake. What on earth did he think he was going to do with them? Beats me, but he saved them for future generations.
Your dad and my dad must have been distantly related.

When I was about three or four years old, we had this old floor-to-ceiling lamp in the corner of the den, which had three spotlights on it with shades. Since it was getting flaky at that time, he removed it. So naturally, 40 years later, guess what we threw out when we cleaned out that basement?
He used to bring home "stuff" from places he worked at. Plus, he had machinists tools, bits of metal, a box of miscellaneous pipe pieces that fit no plumbing in the house, and a lot of old things that had broken down over the years. He had an entire (but outdated) set of the Thomas Registry books in hardcover, plus a cupboard full of old manuals and papers from various workplaces. Since he used to work on automotive interiors, he had brought home a ton of vinyl remnants. Plus, we had three industrial sewing machines, one a double-needle. (I had a buyer on eBay, down south, ship me up a wood crate three separate times to send those down to him.

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Oh, and did I mention he used to make champagne? He had at least a dozen glass five-gallon bottles that had varying stages of vinegar in them, not to mention about 14 cases of empty champagne bottles he had collected from friends and relatives over the years for bottling it. It was a great hobby for a while, but then he got too busy with his last job, and then fell ill from a stroke.
A few things I kept but for the most part, whatever didn't go to the Salivation Army was tossed at the curb.
There were a few pieces of furniture I wish I could have gotten from my grandmother when she expired. I got my dads stereo gear when he passed because my mom had no interest in keeping it.
I am still hurting for this...my grandfather built a lot of Heathkits. The audio system he had when I was a tot was one of those integrated amps that now fetch a few bucks on eBay. He had the mono tuner to go with it, and it had an add-on stereo multiplex adapter to play stereo FM. He stuck it in the basement when he built a new solid state Heathkit receiver (which I still have...the one thing of his that I kept). But as for that tubed integrated amp? My uncles tossed the console it was in, out at the curb on garbage night, about 25 years ago. And at the time, I'm thinking nobody would want "that old off-brand tube junk". Duh. Had I known, I would have grabbed at least that amp and stashed it somewhere. (Since he had it mounted in a console, I don't think he had the case for it.)
My mom is still alive and other than her collection of art, her possessions are mostly ordinary and practical, so there won't be much heartache to see it all go when it's time.
Since my mother was a commercial artist throughout her life, she tackled many mediums as hobbies and of course, everyone in the family wanted a piece of it.

I have the pieces she won national awards for. And my youngest is entering art college in September, and she appreciates all of it. So I have a good person to hand it down to.
As to the furniture, which was in really good shape, I couldn't give it away. I offered it to folks in my office, who needed help financially, young kids, or divorced dads, nobody wanted it for the price of renting a Uhaul.
I have a lot of my own hoarding to get rid of (some of it is still from my parents' house, as I haven't had time to go through a lot of it). And as old as it is, I still have my parents' Ethan Allen living room set. It has held up for 43 years but is getting frayed. (At their house, the living room was only used when guests came over.) I am getting new furniture soon.
I mention this because I know that the old furniture and other "stuff" will not sell, but I am going to try both my local Freecycle mailing list, and the free category on Craigslist, to get rid of it. Smaller things I can haul to Salivation Army. Anything else will get picked up by the GFL boys on trash day. (Can't say "Rizzo" around here...locals will know what I mean.

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