The thing that you need to be thinking about most in terms of new colonies is that they are pretty much always going to be the most vulnerable colonies in your entire empire to attack.
This is important, because the computer AI usually targets first the colonies of yours that have the weakest defenses out of all the colonies in their fuel range.
They also prefer to attack the colonies closest to their own borders which, usually, the ones you most recently took over are.
It is not unlikely as soon as you take over one of these colonies they will send ships at it right away.
The number one priority for all new colonies is to get planetary shields and sufficient missile bases constructed as quickly as possible.
You will likely have the vast majority of your fleet sitting over the planet and that fleet will be tied down to the planet's defense until those defenses are constructed. Once the shields and missile bases are constructed, then your fleet will be free to go assist in taking over the next planet.
Sending all your planet's resources right away into shield construction might not be the quickest way to reach that goal, but often it is.
Use some judgement in regards to the number of factories on the planet. If you are above half of your max capacity, its probably better to just go full shields. If you have few to no factories after you take it over you probably want to try to make more before you construct the defenses.
It is not the worst plan to put half your extra resources above cleanup costs into defenses and the other half into factory construction. This is the most easy to manage method and probably the worst. This is pretty inefficient, so you want to only do it after you feel very confident you are well in the driver's seat and you don't have much possibility to lose.
The best, if you like to micromanage, is to just build factories with everything until you think you are ready to go full into defenses. You will ramp up your production fastest this way and get to the point where you can build the shields quickly.
This may sound like it makes complete sense, and it probably does to most people. Some may not make the connection right away, though.
You probably don't want to worry about spending planetary resources to clone people on these new planets. If you really want the people, take them from a full population and well defended planet close by.
Also, it is a good idea to always have money in the interplanetary reserve ready to pour into these planets to enable you to build factories as quickly as possible and to get the defenses stood up as quickly as possible.