Not sure I agree with the idea of a general store though. Technically it's still a military ship (broadly speaking) and with the absence of money I imagine most material requirements would go through the Ship's Quartermaster as would any "snail-mail".
I think in TNG we saw something vaguely resembling a store on the E-D but that was basically a huge replicator for making giant bunnies. For "shopping" purposes I imagine it's usually more a case of the crew buying/trading things on shore leave than the other way around.
Military ships, especially those of the USN, have small stores for crew to purchase things such as candy, magazines, soap, etc. They are mini-marts/exchanges. When my father was an officer on a destroyer, I had a chance to see one. So, I don't think it would be out of the ordinary on a Starfleet vessel. Also, TOS did have use of the credit system as noted in "The Trouble with Tribbles" when Uhura took Chekov to do a "little shopping."