Segel II looks like the best first choice for a new colony to me - Normal gravity, 5 production/worker, 4 max pop.
State of the Empire at inherited turn (3504.0)
We're at 0% tax, and gaining 8 BC per turn. We have +1 food, and 4 free freighters (out of 5 total).
If nothing is changed, we have around 7 turns until we learn Physics (laser cannon, laser rifle, space scanner), 23 turns until our colony ship (being constructed at Kholdan I) is complete, 12 turns until the biospheres on Kholdan II are complete, about 11 turns before Kholdan I gains a population point, and about 26 turns before Kholdan II gains a population point.
Kholdan II:
Kholdan II has one population, can reach 4 population, would likely hit 2 population in about 26 turns, if production were unchanged. We were building biospheres, and had 12 turns out of 13 remaining on it, but the biospheres would finish long before we even hit 2 population. So, I'm reassigning Kholdan II's production to housing, which should bring it to 2 population in about 9 turns instead. We can switch back to biospheres when we get closer to the current population limit (which is 4). (Our other choices for production were a marine base, a starbase, or trade goods - we don't need the marine base yet; The starbase would take a very long time to build; We're already gaining 8 BC per turn with 0% tax)
Kholdan I:
Kholdan I currently has 3 farmers, 6 workers, and 3 scientists.
If we reassigned all scientists to production, we would complete the colony ship in 16 turns (7 less than now), at the cost of having no research for 16 turns, but we desperately need research, so I'm not going to do that.
I am, however, changing one scientist to a worker, which reduces the colony ship production time from 23 to 20 turns, while raising the research time from 7 to 10 turns. I expect the future technologies will require significantly more time to research.
Technology:
I think these researchable technologies are particularly important (in this order):
Optronics - Optronic Computer (130 RPs): +50 starship weapons to-hit
Force Fields - Mass Driver (230 RPs)
Advanced Biology - Cloning Center (380 RPs)
Military Tactics - Space Academy (130 RPs)
Xeno Relations - Xeno Psychology (650 RPs): +30 diplo points to deals offered to opponents
Advanced Metallurgy - Tritanium Armor (230 RPs)
:
We have one scout ship, which is currently at Milaff. I'm sending it back through the wormhole to Segel, for the time being.
Our Physics research has been completed. I have instructed our scientists to research optronics (optronic computer), which they estimate will take 28 turns.
We also have two people on Kholdan II now, and with continued production of housing, we would be likely to gain a third citizen in about 8 turns. However, I'm going to put the new guy on research instead. We should get a third population point in about 11 turns now, and our research time has been lowered to 21 turns.
The colony ship is on schedule to be complete in 11 turns.
3505.5:
Kholdan I has gained another citizen, who is now farming. We're gaining 10 BC per year, and have 3 surplus food. We also have only 3/5 freighters left. Kholdan II has 2,554k people, and is gaining 88K per turn (which is 6 turns to a new citizen - it gains 44K per turn instead if that guy isn't making housing).
I have hired a public engineering firm to complete our colony ship in one turn for the low low price of 228 BC (We now have 105 remaining). While they work on it, I have transferred our 7 workers on Kholdan I to the research division (which previously only had 2 members), where they will hopefully give a boost to our research effort.
3505.6:
The engineering firm has completed the colony ship, and it has been launched towards Segel II. Our scout ship awaits our colony ship there.
Kholdan II is now constructing freighter fleets (as we will need them soon), and has 5 workers on the job - It will take 3 turns to finish them. Our research boost took us from (15 turns with 2 scientists) to (11 turns with 2 scientists), which would save us 3 turns. However, I have assigned 4 scientists researching now, so it will only take us 8 turns to finish. At this rate, the freighter fleet will be complete in 3 turns. (3 scientists would only take 1 more turn for the research, but the freighter fleet would still take 3 turns)
3505.8:
The colony ship has arrived, and Segel II has been colonized. The colonists' first order of business is to construct more housing. Our population there should expand in about 7 turns (if we weren't building housing, it would be 26 turns).
I've reassigned two workers on Kholdan I to the research department to avoid wasting production.
Additionally, our scout ship is now heading towards the nearby yellow star.
3505.9:
First contact!
We have met the Psilons! Their home system is Mentar, and it is the white star directly west of Sal.
I've negotiated a research treaty with them, which should soon begin to boost our research rate. Unfortunately, we cannot trade any technologies with them - although they have deuterium fuel cells for trade, the only technology they will accept for it is advanced damage control, which is completely unacceptable. (They also have tritanium armor, but we can research that ourselves)
Although they liked the idea of a research agreement, they did not agree to my next suggestion - a trade treaty. They may be more amenable later, once we're both done implementing the research agreement's infrastructure.
In other news, our freighters have been completed, and I have instructed the workers at Kholdan I to begin building a second colony ship. I've assigned six workers to the project. We should have Optronics in about 5 turns.
3506.0
Our scout ship has arrived at Juga, and discovered a planet with gem deposits!
Here is Juga:
As you can see, the gem deposits are on a huge barren heavy gravity planet. 6 max population, 9 industry per worker, 3 research per scientist, and +10 BC per turn if it's colonized. Although it has a 50% worker penalty, I think it is very much worth colonizing. It'll be equivalent to a poor mineral planet until we get gravity generators, but the +10 BC, 6 max population, and the promise of 9 industry per worker once it is colonized make it look extremely good.
Kholdan II should gain a population point next turn.
Here's the nearest part of the galaxy as we know it:
By the way, you can click the technology category button (e.g. "Chemistry" or "Construction") in the tech chooser screen to see what technologies we can research in the future.
To my successors: I would be worried about the Psilons stealing our only advanced technology. Perhaps we should train some spies to help guard against enemy spies (Plus, spies may be our only way of getting useful technologies from the creative Psilons). Good luck!
Apparently, there is some flaw in the upload system, as it won't let me upload the zipped save game, claiming that "the file already exists". 
