I'm partial to rebuilding Western Kentucky, but only because they usually have a solid RB corps to build around. Now I think I'm going to do an offline dynasty with Old Dominion and see how that goes, mainly because I think their logo is awesome.
It IS an awesome logo. I considered them too when I was looking for a rebuilding project in the 4th year of my offline dynasty. The nice thing about Old Dominion is they're already independent, which allows you freedom to create as difficult or easy a schedule you want. No messy conference games to prevent you from scheduling a rival during an opportune recruiting week. The other nice thing about being independent is that your conference prestige is automatically an "A" I think, even though it's Independent. Along with that, theres no conference championship for you to play, so thats one less game in your season (Can't recruit that week anyway). You're stationed in Virginia, which makes it easier to recruit southern players based on distance. They've got a weak fight song though, not that it matters when you're playing, but I like to look at all aspects of a team. It's certainly no Notre Dame Victory March, it's not even on par with New Mexico's:
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Fightin' Bob Davies
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The other downside is that the stadium doesn't play in front of many people (Like 19,000 at max capacity, which would take a few really good seasons to reach). It has a unique look though with the semi-circle stands: