Painted Plywood for Outdoor Planter?

Went shopping at the garden center with SWMBO. She sees a nice planter box and trellis, and gets that look in her eye. I am a relative newbie, but I understand when those tools in the basement had better get to work - payback time.
So, I'm building a planter box with a trellis behind it.
Approx Dimensions: box 18"H x 29"W x 18"D with a 54" tall trellis attached at the back. It will hold two 12" round plastic pots. I'm also going to hang a 6" x 12" planter off of the trellis.
The idea is similar to one I saw in Wood Magazine, but I'm adding the trellis. Basic construction: a four-sided 3/4" plywood box with no top and no bottom. The planters will rest on cross bracing of 2 x 4s. The exterior will look like a blanket chest with a hole in the top with legs being fake stiles and rails (of pine). The Trellis will be pine and screwed to the back legs.
I'm thinking actual 1" x 2" supports with 1" wide by 1/2" thick half- lapped grid trellis.
I was originally thinking 1 1/2" x 2" for the suports, but it looked a little chunky. All of this will be primed and painted white.
Questions: 1.     Since it is all going to be primed and painted, can I go with normal plywood or do I need something special? Wood Magazine used MDO, but I'm looking for an alternative. Someone suggested vertical siding, but I want it smooth, not fake tongue and groove.
2.     Do you think this thing will stand up to reasonable wind and storms or is my trellis going to sway and bow like crazy?
Any thoughts are appreciated.
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plywood will be fine, look at all the "yard art" out there and it is holding up well. i would cap the top edge of the plywood. as for the trellis, I would use 3/4" square and no lap, SS screw it together or glue with titebond III.
Tiny Tim wrote:

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BRuce

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'exterior' grade ply (a waterproof glue construct) strongly recommended.

Yes. "One of the above." Either it will stand up, or it will sway and bow. <grin>
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As a pontoon boat owner (salt water) I know a little about plywood out in the weather. The real trick is to be very sure the edges are sealed well. That is where plywood starts to fail. Start with a good outdoor grade paint, thinned a little and soak the edges. I used a small roller and kept going around the sheets until it couldn't possibly take another drop. Let that cure up well and give it another coat. My plywood deck is still OK after 14 years. I did use MDO.
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