That's about what you would have in a standard chop and flip. That's about what I run. Yes, yes you can.
Stock density there are a few ways and all sorts of rules on the web. Keep it simple so I suggest keeping it light.
http://www.backyardaquaponics.com/guide ... -stocking/ For stocking I suggest the link above. You can really turn that into rocket science but keep it simple. Remember to look up your fish before you stock them. Ornamental fish like Koi and Goldfish and those fancy Cat fishes.... they wont stay small. Stock them as if they were their max adult size.
For pump size, you want to cycle your entire tank volume a minimum of once an hour. Always give yourself some leeway because your plumbing, solids, and bio film are going to slow your flow. So a 500 to 600 gph pump would be good.
Other thoughts, I would definitely add a sump tank that's almost a necessity. Easily tuck that under the grow bed. Solids filter are nice but not a necessary. I like to keep my stumps and tanks clean and having a central place to clean it out is nice. Go with the bell siphon.
For media, you want something smooth. Pea gravel or Hydroton is perfect. Look for an average of .25 inch diameter. Remember you are going to be digging in that. You go with pumice your going to have the best exfoliated hands on the block. Look up craigslist and whole sale suppliers for gravel. Make sure you inspect the gravel and take a cup of vinegar with you. Test the rocks for a reaction. You want a neutral media. Pumice would be great to add to a filter though. Lots of surface area for filtration. You could add a few inches of a base layer with pumice then fill with pea gravel. I could see getting the roots out of it being a pain.
Other thoughts. I would be concerned with the outdoors breaking down the wood. So make sure its treated to prevent degradation. I personally use cinder blocks to support my plywood grow bed. Wood is water sealed and the bottom is painted with Flex Seal to protect it from splash back. Its protect from the elements though on my porch. A pressure treat 2×6 will rot through in two years. I know because that's what supported the old grow bed.
Maybe try and a tank then wrap it in wood. So if it does deteriorate and fall apart your tank is good.
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