Noob to noob, I'll try to help, but take my advice with a grain of salt.
First off, Joe Who?
1. Some terminology questions: what is a "picket" order? What does "extended orbit" do?
Picket tells a ship to stay close and watch something. Useful for monitoring jump points.
Extended orbit say to get close to a body, but don't try to land. This could be used for blockading or bombardment.
2. I just spotted an alien in a neighboring system, briefly. Didn't really get any information about it. It's still year one. What should I do about it? I tried to "initiate communication" with no apparent results and I've designed a little armed frigate (3 lasers, 2 power plants, beam fire control, active sensor, and a little jump drive) to go and try to find it again. I figure I'll scan down the other jump points in that system and send one of my frigates to each one in hopes that they can detect where the aliens are coming from or going to. Not sure what to do once I find them!
Be careful. Some aliens aren't friendly, and will bite. Initiating communication can take a while, and doesn't seem to work with all races. IIUC some races start more advanced than you and some less, so you can never be sure. Depending on your start options, there may even be some who start with super-advanced non-researchable techs. Think Anterans and the Guardian if you have played MOO2. My first game ended about year 10 due to some really nasty FAC's attacking my homeworld. My current game is in year 26 (the longest I've lasted) and I can't even run if I meet them.
In any case, I use a cheap (expendable) frigate with good passive sensors to check out any new system before sending in anything important. Sensor range isn't too great early game, so it needs to get close to anything that looks interesting to know. Build several, and expect to lose them every now and then. I would also suggest not building jump gates into any system you haven't completely surveyed, as aliens can use your gates too.
Even if that race cannot be communicated with, leave your diplomatic team assigned to them. They will still gain XP even after they give up.
3. Which is easier to terraform, Mars or Luna? And. . . what's the "recipe"? Or is it actually easier to do Europa or Titan or something?
I've had good results terraforming Luna with 0.1 atm oxygen and 0.2334 atm safe greenhouse gas. Admittedly I'm only up to 0.1964 SGG so far, but it is working about as expected. I could probably finish off with Nitrogen. Terraforming takes a
very long time.
Mars should be very similar, although maybe not quite as much greenhouse gas. I went with Luna first because it had more minerals.
I think the other two would take longer, because they are colder. In general, the lower the colony cost, the easier to terraform.
In any case, the key is base temperature in Kelvin, to determine ideal gas mix, then compare against what it already has. If you are playing as 'human', you need a minimum of 0.1 oxygen and 0.2334 of anything else to be breathable. The 'anything else' is determined by the base temperature. Most gasses warm a little, GG warms a lot, and AGG cools. You can warm a body up to 3x its base temp in Kelvin, regardless of mix. The formula to calculate it is right there on the Environment screen.
4. Are lasers a decent weapon system to focus on? I kind of like the idea of beam weapons (and I have two skilled energy weapon researchers) but I have no idea if there's a difference between lasers, microwaves, particle beams, etc, so I just picked lasers and went with it. Any advice about how to design and configure the ones I put on my ships?
According to wiki
http://aurorawiki.pentarch.org/ Lasers are good all around weapons. Microwaves are low power, but kill shields, and particle beams are best at longer range. Meson weapons are short range and low power, but damage systems. Missiles are good as standoff weapons. Gauss cannons are used for CIWS anti-missile systems.
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And, of course, Erik beat me to the punch. Dude must be related to Spiderman.
(http://aurorawiki.pentarch.org/index.php?title=Terraforming)
