The first thing you should do at the start of the game is scout and figure out where your opponent is and what planets lie between you.

As a rule, if your opponent's homeworld is 4 or fewer jumps from your homeworld, you should always go with military labs, and if his homeworld is 8 or more jumps away, you should always go civic.  If he's 5-7 jumps away, it really depends on the planets that are between the two of you as well as your strategy.

Your first capital ship should either be a colony capital ship (Akkan, Progenitor, Jarrasul) or a carrier capital ship (Sova, Halcyon, Skirantra).  Colony capital ships are more economic, carrier capital ships are more military.

To increase your income, your best choice is to capture new planets.  Be sure to upgrade them with population infrastructure (they actually lose money until you've done this) and build all the extractors you can to harvest metal and crystal.  Later on, trade ports are a good option, but this requires at least half a dozen planets already under your control.

Not true; if you know every economic trick in the book, you can absolutely rip the AI limb from limb.  You only need the first chapter of tricks to beat them.

First of all, this is a general guideline, not a playbook.  Every situation is different.

When an opponent is sufficiently far away, you have enough time to get both your civic techs and then get your more advanced military units on the field before the actual fighting starts.  Of course you want your military ready to contest your opponent, but many maps give you enough breathing space to get some economy up first (particularly ice and volcanic colonization).  As well, every faction is always capable of falling back to carrier cap spam without getting any military labs, which is an alternative when civic labs are absolutely necessary but a rush is very likely.