I just got the game three days ago, and I love it also!! I got locked out of my purchased copy of Mass Effect, I heard this game has some reasonable DRM so I picked it up. No more DRMed games for me....Thank you!!
There are some really good threads in the strategy forum, you just have to dig a bit. One of the things I do differently than you from what I could tell in your brief, is I do not make a fleet early. I send out maybe two scouts in different directions and look for asteroids for early expansion, then use the free Colony capital ship to acquire them.
Once you find the 'roid, you can pretty much send the CS and forget about it, head back when you hear "new colony", in the mean time work on some mil labs, sell some metal, buy some crystal, and start researching your LRMs.
When you get this all done, then start working on the fleet.
Another thing I learned, and it helped a ton, is I started a new game (AI) but I disable the AI team and leave the pirates. Actually if you are really new, you might want to disable the pirates at first... When they have your sole attention it gets brutal every 5-10 minutes... It isn't *that* hard, it is just annoying. Anyway, that would leave you the whole system to do with as you please. You can work on build orders, try out ships against the small factions on neutral planets... good stuff. I played a few games like that to learn stuff, and last night I actually played my first, albeit easy, game and I crushed (seriously over crushed) the AI in about 1.5 hours taking my time. It really was a very realizing game, perfect for after work...
I babbled enough. Good luck.