They really made an attempt to get rid of all the micro-management in this version, which over-all is a Good Thing, IMO. It allows for some truly vast, inter-stellar empires late in the game that don’t take half an hour of work per turn to keep running. However, it does mean that there’s simply not a lot to do in the first few turns.
Mostly, you’re going to be working on exploration right now. You started out with three spaceships: two Scouts and a Colony ship. Send them down every available star lane. When you get to a new system, check out the planets in it. The first thing you want to look for is desireability, which is color-coded. Sweet Spot is the rarest, and the most amenable to your species. Green is good, yellow is tolerable, but you won’t be able to do any farming and your population will be limited until you can terraform the planet. Avoid red class planets right now. Many planet will have Specials, such as rare gems, or electromagnetic fields. Some of these are good, some of these are bad. Unfortunetly, short of colonizing the planet, the only way to find out what these specials do is to look them up in the Readme file on the disc.
The first part of the fame is, as usual, a land grab. Keep building colony ships and colonizing new planets. Try and get a colony in every system you find radiating out from your home system. If a star only has Red class planets, put an outpost on one of the planets so your race has some claim on it, until you have enough tech to make colonies of Red planets viable. If you find a really sweet planet, but don’t have a colony ship yet, use the Send Colony command. (From the system view, click on the planet you want to colonize, click on the Forces tab on the bottom of your screen, and click Send Colony) One of your colony governors will build a colony ship and send it to that planet as soon as possible.
Your home system will usually have a bunch of good planets, too. Build a few SysColony ships (cheaper colony ships that don’t have a warp drive, and can’t leave the system they were built in) and start colonies on the better planets at home.
Your colony governors usually are pretty good at choosing what to build next, but if you need a specific ship as soon as possible (usually a colony or troop transport), you can change it yourself, although it’s a pain in the ass: double click on a star on the galaxy map. Double click on one of the planets. Click on the Economics pop-up menu, then click on the Military pop-up menu. This’ll let you set your own build queues. Until you’ve gotten a better handle on the game mechanics, you’ll probably be better off letting the computer handle this.
The only other thing I can think of that you really need to worry about first turn is espionage, and then only if you start off as a member of the Galactic Senate (which is randomly determined at the start of the game) If you’re a member of the Senate, on your first turn click on the Personnel tab on the bottom on the screen, select Espionage, and build a bunch of spies. Your opponents’ll already be trying to infiltrate your empire, and unchecked spies can do a lot of damage.
Hope that helps. If you’ve got more specific questions, I’ll be glad to do my best to answer 'em.