That quarter currently has $2.75 worth of silver but yeah, a shop would pay only $2...or less.
It's rare to find pre-1965 silver quarters, dimes and half dollars in circulation. There are people who make a small business out of going to banks and buying rolled coin and searching - they literally spend hundreds to thousands of dollars per week, then selling the non-silver coins back to banks. The return rate is extremely low, but for these people, it's a numbers game.
You can get a slightly better return going through rolls of half dollars, but you can't find those very easily. 1965-1969 half dollars are 40% silver.
You might also find an occasional silver 'war nickel' in nickel rolls. Dates are 1942-1945, and only coins with a large P, D or S on the reverse, above the dome, are 35% silver.
There's always a slim chance of finding a scarce coin from any series in your change, but what to look for, the list would be too long to do here. You need to start reading books on coins.
You won't find any crisp older paper money in circulation. The thing to look for there is a fancy serial number. Look up that subject to know what the different types are.