There are several readily available and environmentally friendly products that you could use in framing your project.
First, you need to decide what type of structural construction to use. In addition to typical stick framing there are a number of viable alternatives such as straw bale, rammed or sprayed earth techniques (pneumatically impacted stabilized earth, or PISE), insulated concrete form (ICF) construction, and panelized construction (using structural insulated panels, or SIPs). Each has its own advantages.
Considering the unique demands of straw bale and rammed earth techniques, and that much of their value comes from their ability to perform in environments with wide temperature swings, these are probably not your best options. Also, ICF construction is better suited to areas with extreme temperatures, either hot or cold, and is similarly not ideal for your location.
That leaves either traditional stick framing or SIP construction, either of which is well suited to your regional weather and your experience level.
For SIP construction there are several companies that will use your completed plans to custom design and engineer panels to suit your design; go to the Structural Insulated Panel Association website for suppliers and installers in your region. You then provide labor (and a crane) to assemble the wall and roof panels on top of the completed foundation. When selecting a vendor, look for panel construction using rapidly renewable and sustainably harvested wood sources, urea-formaldehyde-free glues, and soy-based solid foam insulation using non?ozone depleting accelerants. Well-assembled SIP construction can be much more airtight than traditional stick framing. Plan carefully for your assembly and expect costs to be about the same as they would be for stick framing.
If you opt to go the traditional route, there are several ways to maximize the environmental friendliness of your project. As always, look for sustainably harvested local wood sources for your framing lumber?use FSC certified if you can find and afford it. If you can plan your construction for warmer and drier months, you should be able to use green lumber and avoid kiln-dried wood, which is more expensive and involves more energy use in its manufacture. Also, look for urea-formaldehyde-free plywood and sheathing materials (try Columbia Forest Products for a range of alternatives), and use VOC-free construction adhesives for your glued connections. Go to the Titebond site for a sampling of what's available from one manufacturer?or better yet, ask your local lumberyard or hardware store to carry a full line of low-VOC products. Finally, educate yourself in the application of advanced wall framing to minimize your use of materials while maximizing the structural integrity and durability of your project.
For more information:
See GreenHomeGuide's "Are Structural Insulated Panels (SIPs) the Right Choice for Building a Healthy Home?" for a lively debate on the pros and cons of SIPs.