Fiber-cement board is a very sustainable option for wood trim. In fact, the fiber used to create fiber cement is typically recycled and sustainably harvested wood.
The two major manufacturers of fiber-cement siding and trim in the United States are CertainTeed and James Hardie. Both of these companies have web tools to assist you in finding a certified installer.
To your question of the best wood to use: There are many factors to consider when determining the best product. Since I am familiar with the climate and business environment of Massachusetts, I would recommend western red cedar or redwood as the "best" wood products for your project. However, given the cost and availability of these products, I believe you are on the right track with fiber cement.
Both cedar and redwood options are a more expensive alternative to fiber cement even if you are using a finger-jointed product. Many builders shy away from finger-jointed wood based on the unpredictable nature of the wood itself and the seams that are organic to the product. If you have to replace small sections of the exterior for a renovation, finger-jointed products are the perfect solution. However, the cost for an entire home given the unknown behavior keeps many builders/contractors away.
I believe you will be most happy with a fiber cement renovation of your existing trim. The cost and durability of fiber cement versus real wood for an entire home make it a great choice for green siding. If you do choose wood as your solution, consider FSC-certified products to ensure the materials were harvested from sustainable forests.
As a final note -- knowing the area, I suspect your home would be considered a higher-end property. But if this isn't the case and your current trim is not showing signs of rot, another solution is to cover the existing trim with aluminum. This product is completely recyclable, maintenance free, and a great solution to a budget crunch.