Re: What do you do onboard a starship?
Resource Identification and Extration primarily. For aboard ship, (and also once you make landfall) you need farmers. That is your base, your foundation, that you need or else your colony will not survive. But with modern technology, that still leaves a lot of folks just hanging around.
Which goes back into mining, and other areas of resource extraction. You'll need a science team that will be able to indentify any materials the colony comes across. Once you figure what is where, you can decide what is, and is not a resource to be exploited.
So, farmers, a science team, miners. These you will need before any technology is even possible, let alone doable. After that you will need engineers, arcitects, and designers. You might need a government setup which will require people. And Cops and military (if facing external threats)