Hi!
Don't deplete your home world pop too much at the start - it is the only planet that will make you some money. I only send out 100 colonist per ship too start with. Orbit the initial Colony ship to unload it - then launch it with only 100 Colonists.
Sorry, but that's a bad advice for ANY race but Super Breeder. The tax revenue is calculated from sqare root of the population, so additiona 0.5B on your 8B Home world will give you 1 more BC revenue, while on the new planet they'll give you 5BC. Lifting 3B from your HW will result in ~5B lower revenue form it, but spreading that pop to 6 0.5B planets will give you 6 * 5BC = 30BC. Also, at 100% approval a 100M planet will need ~58 turns to grow pop to 3B where it will generate enough revenue to pay for itself, while 500M pop will grow to that number in 31 turns!
Rush an econ building right off the bat instead - much cheaper
With 100M pop and 4BC revenue from the planet that's just riduculous. You build first econ building when its effect shows, and that's when that planst produces ~10BC.
As your pop grows, rush buy 1 entertainemnt building as needed to be able to keep your tax rate high.
That would be good advice if you'd be swimming in money, and you wouldn't have better ways to spend it. In all other cases that's a recipie for bankrupcy, as every entertainment building needs maintenance, that only adds to 14BC manitenance for the Initial colony.
A smart player only rush-buys anything on colonies if his income is positive (or very close to), and he has enough money in treasury. In all other cases the initiall money serves as the bridge from big deficit spending (colony drive runing full speed) to positive cash flow, where your coloniest start contributing money to your empire. Each rush-buying can shorten that bridge for 5-10 turns. Just a few of them, and AI on though will serve you your butt on a silver plate.
BR, Iztok