Nope any pot should work even home depot buckets with holes drilled in the bottom work well. The 5 gallon homer buckets are cheaper then there 5 gallon plant pots.
Oh the other part...you start in smaller pots (i start in 1 gallons) so that you can make a nice root ball you dont get that when you go straight to a big pot.
Why would you want 20 gallon pots for a plant that will only be a few feet tall. You will be costing yourself more in ferts and soil then you need to. Also they dont need that much space. I would use 5 gallon pots.
Flush the F*** out of it....i would have flushed for more then 7 days. what you want is to get a TDS meter and want that number to be as low as possible.