I looked into building a log home (for reals). Obviously, the larger diameter logs have more R value, and in the pacific northwest, everyone recommended cedar because it resists rot(salt air and rain) and bugs. Cedar comes in about every size imaginable. I know in Arizona and warmer climates White Pine is a big favorite. Someone once recommended using a species of wood that is native to the area you're building in.
One of the main reasons we did not use logs in our construction is because the home itself is hard to appraise if you have to sell it. Since it was our primary residence, we decided to go with stick frame, cedar siding, and timber accents.
Another reason we did not use logs is because finding a builder that knows how much they settle, and how to install plumbing and windows with proper spacing was difficult. If the logs are not cut from dead standing timber, then they need to be dried out to help with the settling/shrinking problem.
Keep doing your homework. Home Time on Discovery Channel did a show on building a log home. Great info. Get all the log home magazines you can find and ask everyone you can think of.
Are you thinking of a prefab log home, or one that's put together on site? Alpine Log Homes in Hamilton, Montana has done beautiful things nationwide. Neville log homes, and Rocky Mtn. log homes. All located near Hamilton, Montana.
Good luck!
And on a more serious note, I bought g-damn lincoln logs thinking I'd make one before I built.
I hate those things!