You have correctly identified the problem: how to recover value from a pile of unknowns.
And you have correctly identified the solution: your time goes in and, maybe, some value comes out.
Either you put in that time, or someone else puts in that time.
If they put in the time, they pull out the cash ... not you.
That's not evil; that's just fair.
So: how much time have you got? how much time do you want to put in? at what hourly rate do you hope to get paid?
Q/ When did your great grandfather stop collecting?
If long ago, the odds are that you will laboriously check tens to hundreds of stamps before you find one that pays you minimum wage for the hours it took to get far enough along to find it.
If recently, the odds are that you will check thousands ...
Q/ Are there any artifacts that accompany the collection?
For example, if your great-grandfather bought at auction or from dealers, there might be invoices or, at least, items in glassine envelopes with labels that identify country etc.
This would be a clue that your great-grandfather put some cash money into his collection, raising the odds that there might be some cash for you to recover.
But if, on the other hand, you are really looking at an undifferentiated pile of stamps that look like your GGF (and his friends & accomplices) pulled every stamp off of every piece of incoming mail they could get their hands on then, perhaps, that is exactly what they did and, well, the time-in-cash-out ratio worsens.
One thing to look for (given events in his lifetime) would be wartime (and immediately post-wartime) usages; some of these re-valuation over-prints can be hard to find Genuinely Postally Used, never mind un-forged & un-faked.
And, of course, you said 'stamps' ... do any of the (especially older) stamps come with enough paper attached to show complete cancellations? Are any of them on complete envelopes or cards? Did you spot any with initials perforating the center of the stamps?
Frankly, we all hope that you'll start pawing your way thru the piles, get a little curious, get a little interested, get the bug, and come down into the rabbit hole with the rest of us.
If you like, you can let your amateur eye wander, see what looks old or different, and throw us a few scans. Who knows?