Here goes... though undoubtedly you'll get plenty of advise from far more expert players.
1) I would advise to go for Torian (faster population growth which helps a lot early on) or Korath (military boost and those awesome spore ships)
I usually spend some points on economy and research.
2) Homeworld building order: a simple plan is to rush-build 2 factories, then either:
- go for all economy on your homeworld while using other planets for research
- build some research labs, then economy centers
Once your population has grown so much that morale is down, it may be a good idea to have 1 morale improvement building.
If you have any special bonuses (except food production) on your homeworld, by all means make use of it. Influence bonuses can be ignored as well, depending on your strategy.
2A) Little class 4-6 planets: I usually devote them to research, except for 1-2 (up to a medium sized galaxy) where I have at least 2 factories and a starport for some additional military production.
3) Money: increase taxes, research more economic techs, trade, sell minor techs to AI's, devote your homeworld to economic buildings. Try to get your hands on as many anomalies as possible (some of those 1000 bc ones help a lot early on).
And most of all, choose wisely which planets you colonize (less than quality 5 is often not worth it; you can leave the small one in your star system for an AI to develop, then through influence flip it)
4) Ship designs: you can save your own designs (since the standard ones are quite limited) which is especially handy if you always go for the same weapon branch (mass driver/beam/missile)
5) Research: some basics such as universal translator, stellar cartography; some speed enhancement (with "some" I mean 1-2 techs until the time to research the next is over 10 weeks, then it's clearly time to pursue some other subject first) to grab those precious planets and treasures faster than the AI. Then some population growth bonuses, followed by economy and research.
Once I see the AI has got some military techs, it's time to either trade for those or start researching yourself.
Hoping this gets the discussion started