Superb coins!
I like US coins, but most are too expensive for my blood. Thankfully, relatively few design or composition changes means that many coins can be pulled from circulation. I was able to get all cents back to about 1937, all nickels except 1939-D and two of the war nickels, and about two solid rolls of Buffalo nickels when I worked as a cashier for 4 years in college.
I used to frequent the roll hunting forums of a few other sites; some pretty impressive things can be found in US change.
Also, by zinc cents I assume you mean the 1943 zinc-coated steel? Those are actually dumped into coin counters all the time, but all industrial counters in the US use strong magnets to pull foreign coins out of circulation. Those are the only magnetic coins the US has ever made, so they are the only thing that gets pulled out 99% of the time when they get dumped.