First, your example sentence is a little redundant. Typically, we'd say either:
I prefer money over happiness.
I choose money over happiness.
This isn't to say your example is ungrammatical; however, it would be unusual to see, except perhaps in a special context, such as:
Most people choose happiness over money, but I prefer to choose money over happiness.
That all said, your question seems to be about picking the proper preposition based on two preceding verbs.
Unfortunately, that's not so simple, either.
Don't fall into the trap of thinking about prepositions too formulaically. Selecting the "next preposition" is rarely (if ever) so easy; it's not like we can say, "I'm using the verb prefer, so the next preposition I will use is over." In fact, there are a range of possibilities, depending on what the speaker or author is trying to express.
- I prefer to skip breakfast on Sundays.
- I prefer choosing money instead of happiness.
- I'd prefer to choose money for my main goal in life.
- Some might want a diverse stock portfolio; I'd prefer to choose money in the bank.
- Some people like to put their money in bank; I prefer to choose money under my mattress.
- You're asking me to pick a lullaby in the morning; I'd prefer to choose a lullaby at night.
- Most people take the G.W. Bridge; I prefer to choose the Tappan Zee Bridge to cross the river.
Granted, some of those may sound a little awkward, but I was trying to show the different ways the already-awkward "prefer to choose" might be used with different prepositions.
Normally, though, I think most would say the mattress sentence something like this:
Some people like to put their money in bank; I prefer to put my money under the mattress.