I was recently introduced to Eclipse via Big Daddy's iPad implementation. I've been mainly playing the AI as I try to get the hang of this relatively complex game. I'm getting better but I hope that veterans of the board game version can share some of their wisdom with us iOS newcomers.
While researching the below comments (but after posting the question) I found this excellent post, Five Thousand Words about Eclipse on the Tao of Gaming blog. It has some great thoughts about ship size, virtual fleets, and turn nine.
I thought I would answer with a few of my own observations regarding strategy to start off. Some of this answer is summaries of some articles on the BGG Eclipse Strategy Forum