Ive already tried to do exactly what you are doing and I could find
no source of water valves to suit.
Most electronic water valves come in 2 types, either solenoid valves
or ball valves and both are expensive , like $20 each or more.
Neither are designed to control small water flows with a low head
which is what you get with the arrangement you have in mind.
About the only way I could see to do this is with a water pump for each pot
but even using the cheapest pumps I could find , which are small pumps for
car windsceen washers, you are still looking at around $12 per pump.
The Arduino etc is the least costly bit .