Be careful about buying colony ships early, your home planet has a very low population and those ships take people away. I like to let my home planet build a scout first, dont buy just let it build. By then the population should be up a little and you can buy a colony ship and you can use the scout to find planets so you do not waste time. Research better engines first, and upgrade your ships immediatly. Be careful about the amount of buildings you build early, they cost money to run. So dont build a farm until you need it, if you have a pop of 1 billion and it can grow to 5, you do not need a farm. I build in this order factory, spaceport, lab then if the pop is at 5 billion farm, market, entertianment.
Small planets 6 and under, factory, spaceport, then all the rest factorys. Remember you control taxes, early on crank up the tax until you get a %60 approval rating, remember to watch this and lower taxes as it goes down. Also make sure your production is as high as it will go and leave you in the black. Once everything is running well you should be able to make money with around a %30 tax rate. Important early to not build too many entertianment complexes to make people happy, remember they are pissed at the tax rate, and that will go down as your economy picks up. Rule of thumb for me, for every farm you build you will need a enertaiment building.
Always use the planet bonus, so if you follow my strategy on using only factorys on 6 planets, but that planet has a research bonus, use it. Never use the food bonus on anything less then a 10, unless it is backed up with a entertianment bonus. Never ever under any circumstance use entertainment of food bonus on small planets, they are wasted bonuses. I like to make my large planets jack-of-all-trades early in the game until I have finnished my settler rush, then I will go through and start specializing them. At this point I decide what are my top three planets for production, cash and research. Cash planets should be able to support a huge population 20 billion+ remember you need one entertainment building for every farm, and lots of leftover plots for banks\markets\yada. My main research planet is the one that got the most research bonuses, remember you do not need population for research or production only cash. (I tend to put at least one lab on every planet) . Another thing I forgot is to research sensors early too so you can build survey ships and scoop all those bonuses, I get 2-3 extra survey ships out and its cha-ching cha-ching, always seem to get cash when I need it too.
EDIT also if you are at the top in the most powerful category, everyone tends to suck up with cash and tech. Do not worry about it early, nobody can invade you anyway. I find it funny, every game early on I am busy building up my planets and have no military at all. The drengin see I have none and declare war on me, of course they have none either, so they never attack. I build a bunch of ships quickly become the most powerful civ and the drengin end up giving me a bunch of techs and cash to stop the war that never happened. LOL the drengin decleration of war is my sign its time to switch to military research.