Probably depends on how far apart the supports are spread. Keep in mind home construction has been done for years with 2x4 construction with studs 16" apart. The loads are probably 3-4 times your GH will ever see. I think you're ok with 2x3's but check out sites like sturdi-built and cedar-built greenhouses, i think they use 2x3 construction. Bracing may not be needed but eliminates bad joints and foolproofs the build. A skilled carpenter would probably skip the braces but a hobbyist might be better using them. Make sure your ground anchors go deep enough to prevent frost heave. Good luck with your build.
