Logistic slot/ labs build order strategies?

The first thing you want to do is scout.  You usually shouldn't commit to your labs until you're reasonably certain how close (or how far away) the enemy is.  I've often jumped into civic labs too early only to discover an enemy four jumps away (which can be recovered from, by the way).  The one key technology you're forgetting about are repair bays.  Very high priority item, you definitely want this unlocked even if you don't plan to build them right now.  When you do need repair bays, the last thing you want is to have to wait for the research.

A good opener for Vasari (and sometimes for TEC) is one of each lab.  This gives you access to population upgrades for terran planets, repair bays, and assailants.  This also leaves you one lab away from flaks and ice/volcanic techs, so you can very easily switch to a more economic flavour or more military flavour after further scouting.

Two military labs is pretty much agiven if you start close to the enemy.  Two civic labs works well if you're in the pocket in a team game or far away from the enemy.  Both are viable openers in different scenarios; you have to scout and look at your situation and decide what approach makes the most sense.  Remember that two military labs will get you carriers as Advent, and players usually neglect their light frigate and flak early game, so even Advent can delay illuminators.

Now, the tough part is when you need some of each lab.  Your homeworld has space for two labs by default, and you can probably nab one asteroid very quickly to get a third.  You certainly don't need more than 3 civic or 3 military labs early game, but you may need some combination thereof, and that's where you run into logistics problems.  If you need four labs (commonly 2 civic/2 military, but sometimes 3 military/1 civic) then scuttling your capital ship factory to make room is a good idea.  If you need five labs, scuttling your capital ship factory won't help you.  You're better off finding another planet to colonize or biting the bullet and getting a logistics upgrade.  Once you have one ice/volcanic and one asteroid, you'll have room for five labs; I've never run into a situation where I've desperately needed more than that in the early game.

DArvin raises some good points, but I do things a little differently.

First I always get the logistics upgrade in the very beginning right after I start building my first two labs. My reasoning behind this is with the 8 extra slots I can build 2 extra buildings right away, instead of waiting for my roid to be colonized and then its infrastructure and logistics upgraded, and I wont have to scuttle my cap ship factory right away for space if Im rushed (which could hurt me later If I survive the rush). In a MP situation you can usually tell if you need to go military or econ right off the bat with a quick zoomout and checking the placement of yourself in relation to your allies. In a SP situation it'll require some scouting. Send your scouts out along the outer most path they can (in relation to where the star is) and keep you eye out for enemy scouts and frigates. 90% of the time your enemy will be along this path, the other 10% theyll be 1 jump inward (but youll no doubt spot a scout in this case). After locating your nearest enemies, take a look at what you have around you, how many jumps their are to your nearest enemy, and what kind of militia forces are between you and your foe.

If you have a good amount of neutral extractors, a desert/terran or 2, and/or a couple of non-dead asteroids, its safe to go full military if necessary. The extractors/desert/terran/roids will be able to sustain your military needs for a little while, so build 2 military labs, upgrade logistics and build a 3rd. This will give you access to any tech you need to handle an enemy advance. During their constuction it would be wise to send your scout back to your nearest enemies HW to take a look at what theyre building. Against a comp, most likely it will build light frigates, which you answer with a fleet of lrfs. In MP your likely to see lrfs coming out first (which I always answer with bombers, flak are currently too effective against fighters, plus bombers spell trouble for low level caps). 

If you have a good distance between you and your foe, then its safe to go econ right off the bat. Build two civics labs and upgrade logistics. If you're TEC you wont need a third for some time, Advent- build a 3rd, Vasari- build a 3rd and place a fourth at your roid (leave the last spot open on your HW for a trade port.) This will give you early acces to the trade port tech for any race and you can research it first, and start putting up trade ports relatively quick to get your high powered econ started. I always upgrade my roid logistics for extra space for tradeports in this situation. As TEC you can get 3 ports at your roid and two at your HW by the time youve cleared a 3rd planet for expansion, at which you can start your military or continue with your econ. You can build your econ up until you're attacked (just be sure you have some military labs so you can get military on the quick) at which point your superior economy will allow you to quickly match and beat your opponents forces.

The tricky part is when you're close to an enemy but only have Ice/volcanic planets in your immediate area. You'll need enough labs to build lrfs and two civics labs to research the colonizing tech. Build your military labs first (purchasing the logisitcs upgrade afterwards) and then build your civics labs. If you need to build the second civics lab at your roid (for advent). Build a few lrfs to assist your cap ship with the ice/volc militia (2-4 should be plenty) and then research your repair platform tech and the proper colonization tech. Build a repair platform at the closest planet to your enemy (could be any of the three you currently control) which will allow you to stave off any advance the comp might make at this point. If you do encounter an early attack at this point, pump out lrfs until the comp decides to retreat and you're good to go.

Something I should mention, because I see  a lot of SP players make this mistake when they first join MP, upgrade infrastructure on your colonized planet IMMEDIATELY, 1 upgrade for roids, 2 for all others, otherwise the planet will continue to take money from you. Thehjn point of taking planets is for their economic benefit. You wont be getting that benefit unless you upgrade your planets infrastructure..

Good luck

Ahhh back in BETA or was it ALPHA even, labs were only 3 logistics. This kinda gave you a lot of strategy as to the best dispersal of structures. Also there were no Military and Civilian labs, only trees. All of them used same labs and it went up to 15 labs I think! Good times.

Heck , if your playing the AI skip everything and just get carriers and HC and go pawn.

Thats what i do.The AI will be researching for 2nd cap ship while you are building 5 labs, carriers and crusiers. You should have plenty of time.

Build 2 turrents and 2 repair bays on would be threatened planet and that should hold the starting AI rush at that planet.

                I have to build that because I build no mass of little ships in beginning of game and if enough cash hanger defence also for the seige frig rush (usually 5).

                  I know if AI had scouted my frontier planet HE WILL attack it just a matter of time. So make sure you up defence. The money I would have spent on ships went on teching up and colonizing (planet pop upgrades only, and maybe 1 tactical upgrade on frontier worlds).

                 I would never try this against human player thou, the players here are much to smart!

I try to put off buying logistics slots for as long as possible.  When I get a new planet I'll use it to increase my tech (civilian or military as required), but I try to always leave a slot for a trade post.  Doing this, I use my rate of expansion to regulate the timing of my teching.  Of course, there usually comes a point where you need a speicific tech to deal with an emerging situation, and at that point I'll buy the logistics upgrades.  If that doesn't happen then I'll start getting the upgrades when my economy can support them (usually getting a decent fleet up and running takes precedence).  What seems to happen most often is I'll progress gradually until the mid game, and around the point I have 5 or so of each facility I'll just blitz on upgrades and max both tech trees out.

As usual, scouting is key here - if you know how much stuff your opponents have got, you know how far ahead/behind them you are fleet/economy wise, and can use that to govern your actions.

N.B. I almost always scuttle the cap factory after first cap.

If you are playing against AI, first of all, I find that one of each type of lab per planet until you get ten (eight out of necessity, two for back-up) is sufficient, and it leaves room for refineries, trade ports, and broadcast centers. Always upgrade the first few planets you colonize just to the point that there isn't an underdevelopment tax, save the important crystal for other uses. I find that ONE scout is sufficient to explore, save your metal for research and combat frigs. Once you have a couple (about three) of each type of planet, your economy should be powerful, and once you have plenty of credits, make sure you keep an eye on the black market. Its always a good idea to buy 500 crystal (use shift) whenever the price hits rock-bottom, it makes it more expensive for the AIs, and the crystal is important for research, expansion, and cap ships.