Get rid of all life support stuff, it's useless overpriced junk. Your general colonizer wants to have 1 colony module and an engine or two. Don't add anything else to the hull after that. Make sure you have everything set to 100% manufacturing and 100% military production. Rush-buy as many colony ships as you can until you run out of money. Point them directly at the nearest unexplored star and let them go. And never put more than the minimum number of people on a ship.

When i  rebuild a stripped colonizer its range is not much left anymore when i remove all life support,.. it seems to me impossible to have no life support anymore, because that equipment is needed for a shiprange
I must use at least one lifesupport to get a shiprange of 23,4 ..probably 2 life support is needed for a workable shiprange 

Or maybe stiil using 4 life support modules, but removing a another part and add a hyperdrive.. so this colonizer has it range and goes faster  

As with all 4X games, the direction in playing is up to you. A lot of people fall into the "too much choice, not enough focus" problem which was(is) prevalent in the Civilization series. Going into the game with a clear idea of which winning condition you want to pursue helps you pick not only your race, but also your starting tech choices and settling strategy (or vice versa, which race you pick helps you narrow down the winning conditions you choose to pursue). Not all plan's survive contact with the enemy though, so those plan's may change mid game depending on the situation in the universe but at least you have a relatively focused goal at the beginning.

For example, my latest game I chose to go for a Tech victory as I have not done one yet. So my initial strategy was to settle and secure my own little corner of the map, focus 2 or 3 planets on production/coin (they can share that role - I don't need vast amount's of ships to conquer the galaxy, just enough to defend myself) and the rest on research with just enough production to get the research building upgrades in a reasonable amount of time. Tech choice wise, a heavy focus on research and economy techs was the choice, with just enough military techs to keep my fleets current for defense. As my fleets will only ever be defending home territory, the entire life support and invasion lines are useless so I don't need to bother with them. 

Try picking a winning goal first and then focusing your builds/tech/fleets on that goal and you should have a bit more direction in your game-play. 

Another suggestion I have, in regards to the ship designer, is to filter by core and obsolete every single design as it becomes available. The generic ships are, in general, terrible and shouldn't be built. Design your ships based upon what you need RIGHT NOW. If you need to build a starbase 15 tiles away to claim some resources that are about to be stolen by an AI, build a constructor with 4 or 5 engines to get it there asap. If you are building economic starbases in the back of your territory then you probably only need 1 engine, maybe 0 and you certainly don't need life support. If you need to clean up pirates and they are using beam weapons and shields, design a small/medium ship with missles and engines. You will pop them before they fire at you. What I am trying to say is, tailor make your ships like you do your tech choices. There is no reason to incorporate items on your ships that you do not need, like life support and sensors if it is operating in your home territory anyway.

Ok i get now 13 colonies in 30 turns ..not much difference without the default colonisers versus the different custom colonizer combined..disappointing.
Well again with coloniser, but minimal with a different range..

Every strategy has it's own requirements and all of them will need some form of manufacturing, research and income. My point wasn't necessarily telling you to try a research victory instead - you can choose whatever you want. My point was to pick one from the beginning and try to make sure your choices all build in some way to that particular goal. That gives you a sense of direction and focus so you don't feel too lost. If you are, for example, going for the conquest victory then you will probably find the diplomatic and trade research paths less useful than in other types of games. As you have already said, the bulk of your research will be going into military type stuff. I don't, however, agree that it is necessarily less research than other victory types. Military games will still need a strong research focus - you need to get production, hull types, weapon(s), defenses, invasion, life support (to extend into their territory), engines etc.

Thanks

There is still a lot involved when someone takes the miltiar path..indeed it is difficult to say if this is easier then the other strategies
It seems that i am more familiar with the militair concepts then the other strategies and there is much to learn fpr thr not militair strategies ( if Calactic Civilization 3 can made more userfriendly ? )   

I am looking for a tech tree map as a pdf or jpeg file. I can not see the whole tech tree ingame and i cannot decide where to go.

It would be useful to see the big picture i think.

It requires a trick or two that you haven't figured out yet.

Yup, those two.  Tiny hull for colonizers, and constructor to colonizer trick.  

Well i got now 14 colonies in 30 turns with the custom colonizers models and assigned one sponsor planet to every shipyard..another strategy then assign 5 sponsorplanets to the homeplanet. 
Makes not much of a difference, when i use standard colonizers and use 5 sponsors for the homecolony.

I can start with another tech tree then the one of this race..it should be a research tree focussed on colonising (Thalan?)
I try now the strategy with 5 sponsorplanets for the homeplanet and with customised coloniser and chancing the reseach tree ? 

o yes exponential grow.. y = b • g ^ x  , and logarithms and the number e ..sums ...,  but what is exponential related here? ..idea is that there is a increase of coloniser for every turn

I have choosen terrans ( humans ) , but Thalans is the race what is most focussed on rapid expension of colonies..welll i must make another configurations to platy with this race 
What is the max number of colonies in 30 turns for a Terran race...are there numbers known from other races?...one race could be optimal for rapid colonization 

Exponential grow of number of building turns against number of colonizer ?  
note: i am not a mathematician

Exponential/linear growth of what ? ..not colonyships against turns, but another  quantity..manufacturing against turns ?
I start with the home colony and 5 sponsors
Money...enough money means rushbuy ships..building time ships decrease via sponsorplanets
Coloniser trick and tiny hulls, somehow i must go withinthe 30 turns to the 100% research ? 

To be capable of getting more then one coloniser per turn i must use a sponsorplanets --tine hulls rush buy i need research..benevolent gives 150 research points 
Also here no direction where to go ..to get 30 colonies in 30 turns..perhaps it is related with the population for a colony rush 

I am not getting further...