Took me two months after @EPonMantel challenged me to "do it!", but finally got through sorting, lifting and mounting my grandfather's stamp collection passed down to me when I was a child, and basically stored in a box in bags and envelopes for 50 years until now.
My paternal grandfather and his family fled Russia in 1918-20 as part of the White Army (Don Cossack Republic) resistance forces fighting the communist take-over of Russia. They lost, horribly, but those who survived and managed to escape roamed around Europe for decades only to then be subject to Nazi occupations through WWII. (My maternal side suffered the same fate but were in the north, non-military aristocracy. Their main threat in Russia/USSR was execution based on their last name and cultured upbringing). Both families made it to the US in the 50s.
One interesting thing for me here is the shear number of countries represented. 147 countries. All but a few are canceled (used) stamps, so taken from letters written to them or to friends from friends and family in that Russian diaspora in those 147 countries. Some I still have the full card or envelope, which to me are the most personally valuable, given I knew many of these people now gone. The collection really tells a story of 20th century emigre life wandering Europe as immigrants wherever they went (until our wondrous nation accepted them as its own.)
The collection itself is estimated at about 9,000 unique stamps, and probably 11,000 total with duplicates. To @nando 's observations, the dollar value is estimated at no more than $2,000, assuming an average 5cent/stamp valuation. I've found a few (see photos) that hit double or even triple digits, so it may be in the $3-$4K total. I've got seven of one German stamp that varies from $50-$5000 depending on hue and condition, so might have a winner there.
Another thing I noticed is that while the first stamp was issued in 1840 (GB "Penny Black") stamps remained purely functional for a while. It was somewhere in the early mid 20th century that nations realized people are collecting these things and not using them. That led them to issue more stamps than needed for actual mail, and to issue them in increasing variety to gain revenue without any expense attached since they were not used to mail anything.

IMO at that point, stamps became more like "collectibles" like today's cards are: issued to be collected rather than for any other real purpose. But at the same time, they were never issued with intention to drive up their value like cards (since they are a form of currency after all) so not really all that "collectible" in today's sense. IMO it was in the end not a net improvement to what had been a laudable, if obscure hobby; it didn't increase their value by design (face value rules) while simultaneously devaluing them once used due to oversaturation. At least bank notes didn't get overprinted (too much) an so increase in value over time as they are pulled from circulation and destroyed. Stamps don't get destroyed and keep piling up on the supply side. A such, stamps are not really "collectible" the way that term is used today. Jackpot stamps are few and far between and mostly known at this point. Stamp collecting, IMO the market bears this out, are about either completism (get the whole series just to have it) or then a story about the collector who put it together. The two aspects are not mutually exclusive. But it's not about investing in any way.

I've added a few photos here, will add more specific ones as replies to comment on the stamps themselves for any interested.
FYI: Stamp Identifier app was really helpful in ID'ing stamps, mostly for the year of issue to get them sorted. It also links to Colnect.com for more detail, values and links to ebay auctions. Super helpful app. Free use is allowed if you can tolerate ads every time you find a stamp to get to the ID page.
@samperley by the looks of it, your collection has a lot of the same feel to it as this one. Would be curious to hear how your grandfather arrived at so many varied stamps.
@Aris thought you might be interested (or are you only notes/coins)

I’ve developed a weird obsession with GPK offshoots, like the giant cards and the buttons. So I got a giant Nasty Nick from this guy and he threw in a Weird Wendy for free. I’ve never had that experience on eBay before

Welp, proven to be a sucker again. Saw these cards at the bookstore. Dropped $19 on the lot, thinking maybe they’d be fun rips. Even tried the gum- not recommended!!!

I don’t collect Star Wars but this uncut 1977 series one sheet Heritage is auctioning off is insanely cool.

https://sports.ha.com/itm/non-sport-cards/lots/1977-topps-star-wars-series-1-uncut-sheet-with-132-cards-two-complete-sets-/a/70006-59817.s