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 certail
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.

Contacting League Members
  * 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.

Exploring Space
  * 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 cangive 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 figh 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.

Congradulations! You've won the game!