I work for a company, but we work on science missions. We don’t decide what the missions are, we bid for them, usually from somewhere at the top of the “science community”.
So few things to unpick:
science community – for me, it’s ESA. They ask various science institutes (universities and the like) what they think will be the big topics in science. Those ideas are collated and groups will look at what things might be possible.
Next up – from those ideas they decide to take further, they go to companies and ask for bids. A bid is that companies best idea of what the mission will look like: the satellite, what science it will do, which different companies and countries will work on it, how much it will cost and when it will be ready.
After that – we get our hands on it and divide up the work to make sure that we can meet whatever we have said we will.
In the first place – we consider what are similar missions, or parts of missions, and then come up with lots of ideas for the new thing; at which point computer modelling really starts to help us work out what might work and to start refining things.
There’s a lot in there, so I think I’ll leave it there, but do ask more if there’s more I can help with.