Disclaimer: I have absolutely no affiliation with Star Control 3. Star Control 3 is made by Accolade. I am just an above average player. : )
Please note: The game can be one in many different orders. The first time I played the game through, I followed a different order to win the game, and even skipped a few things. Also, be aware that somethings in the game are time based, and appear a certain number of days after you have completed a certain task. If you can't progress, save the game, and wait a few game days and see if anything happens.
Go to Helios 3 (duh!) and talk with the Earthling base commander. Then proceed to Helios 4 and fight with the Daktaklakpak. Take the artifact there.
Go to Goshen 4, and talk with the Spathi.
Go to Astarte 1, and talk with the Syreen
Go to Salacia 2, and talk with the Vux.
Go to Janus 8, and talk with the Mycon.
Go to Arcadia 6, and talk with the Pkunk.
Go to Formalhaut 5, and talk with the Utwig. At this point, you may receive a distress call from Janus 8. You should go there and talk with the Mycon, then with the Vux.
Go to Velpunia 6, and talk with the Ur-quan. Make sure to take some/all of the ships there.
Go to Hypnus 2, and talk with the Chmmr.
Go to Nyx 1, and enter the Quasi-space portal. You'll meet the Orz. Then go to Muhlifain 7, the Orz homeworld.
Make sure to take the Ebon Hinge on Muhilifain 2.
Wait until the Picus system dissappears, and then go there.
At Astarte 1, you can converse with the Syreen about the Orz.
Go to Izanagi 5, and talk with the Vyro-Ingo. They won't join you, yet.
Go to Typhon 3, and talk with the Harika. They won't join you either.
Go to Enkidu 7, and talk with the Claircontlar. At Enkidu 4C you can get a conc rock. You can give it to the Claircontlar, and get more from Enkidu 4C, but they still won't help you, yet.
Go to Argus 5, and talk with the K'tang.
Go to Cerberus, and talk with the Doogs. Note: There are several Doog worlds, any of them will give the same results.
Go to Anshar 3. Be prepared to fight the Exquivans. Talk to them afterwards.
At this point, the Eltanin system should collapse. (You might have to wait a bit. Maybe not.) Be prepared to fight a long battle!
Go to Goshen 4. The Spathi will complain a bit.
Go to Janus 8. Confront the Mycon about their deep children. This happens after the Earthlings find out about the Mycon. (Time related, I think) Go to Janus 1 to talk with the deep child. Then confront the Mycon again. They will leave the league, so pull Mycon off the Deep Child ship to start a new colony.
Go to Formalhaut 5. The Utwig have lost their Ultron. (Time related...)
Go to Goshen 4. The cowardly Spathi will quit the league. Come back, and threaten to attack them. They will tell you many secrets. Make sure to come back several times and say, "Got any hot tips?" They will tell you many different things, even though you've said the same line before.
Go to Salacia 2. Confront the Vux about the Ultron.
Go to Argus 5, and talk with the K'tang to learn some new things.
Go to Zosma 6, and talk with the XChaggers.
Go to Arcadia 6, and ask the Pkunk about it.
Go to Erato 6, and recover the Ultron from the Vux by force.
Go to Salacia 2, and confront the Vux again.
Go to all the Doog worlds, and buy their colonies with RU's. You'll need about 10,000 RU's per colony. Afterwards, talk with the Doogs, and get the Anti-matter Containment Grid.
Go to Zosma 6, and get the XChagger ships to hold the lost dynasies of XChaggers.
Go to Typhon 6 and Gienah 1, and cure the Harika plague.
After the Chmmr have been bifircated, (not by you) go to Hypnus 2.
Go to Astarte 1, and have the Syreen revive the Chenjesu.
Go to Arcadia 6, and ask the Pkunk about the missing Ultron pieces.
Go to Nebusta 1 get an Ultron piece. The other piece is on Caduceus 4, use it to fix the Ultron. Take it to the Utwig, but you'll find it's still broken.
Go to Mnemosyne 1, after the Harika plague has been cured. Get the Anti-matter Scoop.
Go to Anshar 3, and reason with the Exquivans.
At this point, the Tyche system should collapse. Go there to check it out.
Go to Astarte 1, and learn about the Exquivan situation.
Go to Anshar 3, and confront the Exquivans.
Go to Arcadia 6, and check out how the Pkunk are doing.
Go to Astarte 1, and have the Syreen mind-wipe a tech team to explore Anshar 3.
Go to Anshar 3, and use the tech team to explore the planet.
Go to Astarte 1, and check out the Pkunk again.
Go to Anshar 3, and learn some stuff on the Exquivans.
After the Vux have been revealed as traitors, go to Salacia 2 and kick 'em out of the league.
When the new Q-Space portal is discovered, to Azazel, and use to portal to travel to Haven. Be prepared to fight the Lk.
Go to Antaeus 1, and get the Red Spiral Rail. Then go back to Q-Space G and give it to the Lk.
Get a conc rock from Enkidu 4C, if you don't have one, and show it to the Lk. Go to Enkidu 7, and threaten the Claircontlar. Lure them to Enkidu 4C, then return to gain information from them.
When a beacon is discovered (time related), go to Callipe 2. Wait until Plexor arrives, then talk with him.
After the Arilou tell you to, go to Izanagi 5, and ally with the Vyro-Ingo.
After you get the Vyro-Ingo DNA model (time related), take it to the Lk at Azazel. They will tell you some stuff on it.
Go back to Izanagi 5, and talk to the Vyro-Ingo about the DNA.
Wait until the Vux DNA is discovered. Go back the Lk, and ask them how to join the two. Join the DNA, and show it to the Vyro-Ingo. Take some of their ships, and go to Salacia. Select a Vyro-Ingo ship and send it to Salacia 2. The two races will join together. Go to Salacia 2 and talk with the new Vux. They will give you the missing piece to the Ultron. Take it to Formalhaut 5. (Note: The Ultron does not need to be repaired to win the game)
Go to Goshen 4, and talk to the Spathi. Be prepared to fight them.
Go to Mnemosyne 1, and you should be able to get an Anti-matter Explorer from the Owa.
Go to all 9 of the rainbow worlds, and use the Anti-matter Scoop to collect anti-matter into the Anti-matter Containment Grid. Collect any artifacts you come across. You will find the Mother Ark.
Go to Zosma 6, and have the XChagger fix the Mother Ark.
Go to Hypnus 2, and revive the Chmmr. You will need the Mother Ark and the Sun Device from the Lk. (Note: I don't think you have to revive the Chmmr to win the game)
Find a Daktaklakpak ship and talk with them. Let them come to you. After one game day, if they're not moving, they won't come. If you come to them, they will attack. Some systems where they come to you are: Penates, Themis, Scylla, and Lachesis. Trade with them for the Variance Key.
Go to Begregren 2. Wait until you get a message about the Ortogs from the Earthlings.
Go to Zosma 6, and ask the XChagger for an Ortog.
Go to Begregren 2, and use the Variance key. You should get the Deflector, and the Sentience Notation Device. You can give the Deflector to the Lk, I don't see what good it's for. Nothing happened when I neglected giving it to them, though.
Go to Anshar 3, you can get the Exquivans to join you.
Go to Janus 8, and revive the Mycon.
Find the Daktaklakpak, and trade them for info on the K'tang. Trade them for the missle.
Go to Argus 5, and use the missle. The K'tang will join you.
Go to Pauguk 4, and get the Ploxis ships.
Go to Xipe (time related?), and the the Ploxis rebels and the Sentience Collator. Revive the Ploxis. (Go to Pauguk 4, if you didn't take any ships)
Go to Highpoint 1, and jettison the Anti-matter Containment Grid. Be prepared to fight Plexor's Precursor vessel.
Wait (at Highpoint?) for the Orz to show up and leave the league. Be prepared to fight them.
Wait (at Highpoint?) for the Arilou to show up and talk to you.
Wait at Highpoint until the Heralds show up. Be prepared to fight them. There are many of them, and are hard to beat. You'll get the Sentience Threasher.
Combine the Theasher, the Collator, Notation Device, and Ebon Hinge. Travel to 13 different homeworlds. Come back to Highpoint 1, and use the Sentience device.
If you still have questions (and/or comments), e-mail me firstname.lastname@example.org