Karen, my first thought (seeing NM and AZ as your location) is "not enough humidity". You're going to struggle with orchids there especially in the summer. The high altitude will also be a difficulty, since your thin air makes the sun more intense, and the air is also less able to hold moisture.
Your greenhouse will be great for the cooler months, but most orchids can't take temperatures above about the mid-90's and really want high humidity. I think you might find yourself schlepping your entire inventory of orchids into your sunroom for the summer months just to keep them alive. Then you'd be babysitting them to keep the humidity up in your (presumably air-conditioned) house. No way they'd survive being outdoors in your dry environment unless you tended them constantly or set up an automatic mist system.
Hmm, speaking of mist systems, do you have a swamp cooler for your greenhouse? They work great for cooling and moving air in dry climates.
My daughter lives in Utah, and has been wanting to try growing an orchid for years. I recently bought her an Oncidium 'Sharry Baby' at Trader Joe's (their prices are reasonable) that so far (6mo. or so) has done fine living in her bathroom which is for sure the highest humidity room in the house. They both shower daily, and she mists the plant fairly often, too.
All those Phalaenopsis (aka Moth Orchids) that you see for sale at the big box stores are really not well suited for your purposes, and in fact I don't think they're particularly easy orchids for beginners even though they are sold as such. They need indirect light and moderate temperatures, neither of which you're going to find easy to supply. Go for orchids that can tolerate very bright light and don't mind drying out somewhat - Cattleyas come to mind.
