I think that you will need either a mixed (my preference) or a command economy.
I think that 10,000 is a bit small but it is at the very edge of the smallest gene pool for the new colony. Along those lines, I'd recommend banks of frozen embryos or sperm & eggs.
Also, what is the job of the mission? It is to create a viable colony. What do you need for that? People with the training and resources to start a colony from scratch. And, you also need to get them there. Everyone who is not going to be of functional, working age upon arrival is just a resource. The "payload" is the generation of 15-40 year olds that will be building the new colony.
This might mean that the economy needs to shift between the first half and the second half of the trip.
So, what does the economy have to incentivize? Maintaining the ship and maintaining a system that will produce the best "landing generation" as possible.
If you don't have separate crew and civilian distinctions (which would cause conflict both on the ship and in the new colony through class wars), you need to get people to maintain the ship, maintain the inhabitants, and prepare the landers.
Money could be either computer stored "credits" or anything physical that can be easily traded. A neat thought would be for the money to influence the percentage of resources the landers get on the new world. That way even the early generation(s) has an incentive to make money so they can pass it to their children to give them a better chance of success. Also, even of you don't go that last route, if you don't provide money the people will create it themselves.
I suspect that unless you go the completely authoritarian route, that you will have a mixed command and free market economy. For ship maintenance work, a certain amount has to happen or everyone dies. So, the prices of that will be set high enough that you will get enough people to do it.
Teaching (unless you have automated courses) will also need to be incentivized as will medicine (again unless automated). I would avoid such automation since it would train people to be less than self reliant. A free market may work here or you may need a regulated market (controls that kick in if things go out of balance).
There will also be entertainment jobs just to keep people from going nuts. This will be free market. The people will create it even if it is not provided and they will create some kind of money to pay for it (or barter their rations for it).
One reason to go with the "credits" type of money is that it can take into account disruptions to the system. If someone comes up with a method that allows the colony to do more with the current resources, you can create extra credits to give to that person the increase. That would incentivize that sort of thinking and give the colony the best chance of success.
You might end up with a significant research section in the ship.