Jason,
Here's what I do (currently anyway):
First of all, as soon as you see Sol with your first colony ship and your survey ship, save the game! Call it something like: Save000. Keep this throughout the whole game in case you want to start over for some reason.
The first thing I research is Communication Theory. I want to head for Diplomacy so I can change my government to Republic. Being a Republic allows you to build things faster. The first ship I build is a Scout.
As for the sliders, set Government Spending to 100%, set the Tax Rate up until the Approval rating goes just below 100% and then set it back until the Approval rating is at 100% (around 50% Tax Rate or so). I set my Social slider down to 0%, my Military slider to 66%, and my Research slider to 34%. Some people set their Military slider to 80% with 20% going to Research, and other people set their Military slider all the way up to 100% to really crank out those colony ships. I like to keep my Research going.
Now, send your starting Colony ship away toward a cluster of stars. Send your survey ship in another direction. You're looking for those nice yellow stars with some decent planets to colonize.
Be sure you have Autoturn turned off. I also have Autosave turned off. I save my game after I finish each turn in case I screw up, I can go back to a previous save. I name them s001, s002, etc. I keep 10 saves and start deleting the oldest ones when I have more than 10.
Now, I think you've done everything you can do in your first turn, so hit the Turn button. It will take a couple of turns to build that scout. When it is built, change to building a Colony ship. Now, send your scout off to look for more yellow stars. Also, you're looking for the Alien races.
I don't necessarily colonize the first yellow star I find. What you really, really want to do at this stage of the game is find as many yellow stars as you can as quickly as possible. So, head your starting colony ship out as far as you can looking for yellow stars. Also, your survey ship and your scout, looking for those yellow stars! In the meantime, your building your first Colony ship. Takes about 3 or 4 turns. If your lucky you might find a really good planet to colonize during those first few turns. Like a 23 or higher. Now, when your first Colony ship is finished, double click on it, put 600 M colonists in it, and launch it. Send it off to that star with the really good planet in it (if you found one). Otherwise, send it to the best planet you've found so far and colonize it. This is one of the reasons I do the "Save000", so if I find a really good planet, I might start over and shoot for that star with my 600 M colonist ship.
The reason you have a 600 M colonist ship on a good planet is because your going to use that planet to build colony ships, too.
Now, Earth is just cranking out colony ships. Put at least 200 M on each one. No more than 200 M. Send these colony ships out to start colonizing the planets in the yellow stars you've found. Also, go ahead and colonize a planet with the starting colony ship you had at the beginning of the game. Also, have your other big planet start building colony ships, too. (The 600 M one). Just put 100 M colonists on them, though. You don't want to deplete it of all its colonists!
I like to build a scout on each of my first few planets so they can head off looking for those valuable resources that you want to put Star Bases on. Build as many scouts as you can afford, not too many though, they cost 1 BC maint. each, which is alot at this stage of the game. About 4 or so. Just build 1 scout on the planet and start building Constructors.
Constructors are very, very important in this game. You're going to be building alot of them. They are used to create and update Starbases. Starbases are extremely important. When you find a Resource start heading a Constructor toward it as soon as possible. When it gets there, build a Starbase on it. Also, build a Starbase in each sector where you have a colony. Update these Starbases with more Constructors as you can. Very important. These Starbases can be the difference between winning or losing the game. As you learn to play the game, you'll find out why they are so important. I can't emphasize enough how useful they are.
Now, keep in mind, on each turn you should be looking at your Domestic Policy screen to make sure that you're keeping your Approval rating up to 100%. You'll have to adjust the Tax Rate to keep the App. Rate up. If you don't mind micromanaging, you'll be able to raise the Tax Rate up a little bit every time you launch a colony ship. This is because a planet's Morale goes up when there are fewer people on it. Then you'll have to lower it again in a turn or so to keep that App. Rate up. Micromanaging!
After you discover Communication Theory, go for Universal Translators, then for Diplomacy. When you get Diplomacy, you will be able to change to a Republic. This will let you build colony ships faster. Unfortunately, about this time your Treasury is starting to get dangerously low. Pretty soon, you're going to have to reduce your Government Spending slider so you won't go negative. Maybe by now, you've found 10 to 15 good planets to colonize. Only colonize planets that are 15 or higher. Otherwise you'll have morale problems.
When your Treasury gets down to 0 to 200 or so, you need to change all of your sliders. Set your Tax Rate to 33%. I keep it at this rate the whole rest of the game. Set your Military slider to 33%, your Social slider to 33%, and keep your Research slider at 34%. You may want to change these sliders from time to time during the game. To crank out ships faster, or to finish a social project ASAP, or to research something faster. Set your Government Spending slider down until your making 3 or 4 BC a turn in the early part of the game. Always, keep checking your Government slider to make sure you have a positive number.
After you get Diplomacy, it gets more complicated... You're going to want to research Trade, of course, so you can start trading with the Aliens to make some money. But it may be a little early to do that right now. Another thing is to research Propulsion Theory, Cold Fusion, and Impulse Drive so your ships will go faster. This is important, too. Also, you'll want to research Defense Theory and Deflectors so you can build some defensive ships to keep the evil Aliens from bothering you in the early game. Decisions, decisions. You're going to learn alot more than I can possibly tell you as you play the game. Start in a small galaxy with every Alien race set to "fool" at first so you can learn the game. Work up to larger galaxies and more difficult levels over time. There is so much to learn, but you'll get there. I did. And I'm not a good game player at all! By the way, if you really, really don't like your starting position you can hold down the Ctrl key and hit the N key. That changes the whole dang galaxy! Have fun!