I had a similar question and started a thread for it several years ago. I will see if I can find it and post it here. @CoinObsessed18
I get at least a roll of ATB quarters from the San Francisco Mint every time they come out of the Mint and put them away. You will probably never see them in circulation and ususally have a low mintage. I live on the West coast and we hardly ever see P minted coins for some time and they are usually well circulated, so to keep up to date on the 10 albums I have going for the grandkids, I get a bag of P minted quarters each time also. I have been finding a lot of minor errors each time also. Keeps it fun. I'll let them figure out what to do with excess when I am gone.
No modern coin is going to appreciate significantly in your lifetime. They are made by the hundreds of millions and billions. Even the so-called rare ones are made by the hundreds of thousands or millions - and have a 100% survival rate. For comparison, the low value common coinage of the Romans (2000 years ago!) can still be purchased for a few dollars each. Today's coinage will never appreciate beyond that.
Took some digging, but I found it. Take a look. I’m not exactly sure what kind of information is in there as I haven’t looked at the thread since 2011. @CoinObsessed18 https://www.cointalk.com/threads/mordern-coins-to-future-key-dates.196037/