My stratagy is to continuasly by new colony ships from my homeworld and send them to as many planets I can grab. This usally brings me into debt for a while but itt works out for me in the long run.

While certainly possible with every race in one way or another, I think 2 races are especially predestinated for an extended colony rush.

Those are in my opinion the Thalans and the SuperBreeders (it's the Torians, isn't it? I only used superbreeder together with a custom race so far)
Superbreeding probably got even an upgrade with the recent changes to colony ships (only 250 colonists/module now).

Why do I think those 2?
The Thalans because the factories are incredibly cheap to rush-buy for them. I like to add further heavy economic and production-bonus points to the Thalans, so they can pump out very high production very early. the cheap factories save you tons of money and timeand allow you to chainproduce colony ships very early and very quickly. They are my current favourite race

The Torians because of the economic benefit you will receive from the enormous population growth (if you keep morale at 100%). They won't have a rocketlike start as the Thalans, but therefor perform a much more sustainable growth.

How many planets you can/should grab depends very much on your settings. If you play in a big galaxy and/or with little opponents and/or abundant planets/habitable planets and/or at a relatively low difficulty you can probably grab a lot of planets, otherwise you may struggle and can easily end up with lots of colony ships that don't find a planet...

Personally I had games where I colonized 15-20 planets, sometimes the colonization phase was over after 1 planet (medium galaxies).
But my personal taste is anymore more focussed on conquering planets - which I find to be much more effective than to start a planet from scratch

If tech trading is on, I will colonize as many planets as possible, economy be damned. If Tech trading is off, usually 3 to 4, and extreme environments if I find a worthwhile one. What I really enjoy doing is colonizing PQ 1 planets late in the game and watching them become 15 and 16's because of techs, and the AI basically ignores them. Of course it helps to be neutral for the terraforming.

First off, I don't buy more than the first colony ship or two, as I like to keep my budget above 1-2k. Second, you have to tax your people to the hilt. I mean, have your worst colony at 41% or greater.

Now for two important details that made life much easier for me.

1) Population growth is faster per-citizen for smaller populations
2) Tax increases proportional to the square root of the population

The first point is crucial, what it means is that 10 billion people in 1 planet will grow much slower than 10 billion people evenly distributed amongst 10 planets. People = cash in this game, so you want your people to grow as fast as possible.

The second point is also crucial. 10 billion people will pay more in taxes spread across 10 planets than cooped up in one planet.

Both mean you want to distribute your population as much as possible. Ideal (but not possible in the early game) is to have each planet have the same population. The best way of reaching for this unattainable goal is to build colony ships with 2 colony pods. This means rushing to that engine tech that lets you fit two colony pods.

The reason for doing this is to 1) move as many people off your main planet as possible, so they grow faster and pay more taxes. 2) The per-colony cost gets partially offset by this increased tax income, and you're that much closer to a break-even point. With substantial econ bonuses, you can actually come close to breaking even with just the initial half-billion colonists.

I'm not a big fan of the 100% happiness tactic early in-game, because you can match/exceed that growth rate with just a few colonies, and it means little/no tax income. Tax your people to the hilt, get them distributed across multiple colonies, and you should do fine. I did this with humans, no econ bonus, and only had to drop my % expenditure a few times (mostly because I spotted a resource, and rush-built a constructor).

Oh, and a final tip: That first colony ship you have? Park him back in orbit around your home planet, then ship him out with 250 million people. Your tax income won't notice the decrease in people much, but 250 million people on the first planet you colonize will pay much more in taxes than 100 million, and will offset more of the per-colony cost. Again, this is because you get more tax money, per citizen, for smaller populations.