The canon is full of seemingly contradictory evidence as far as whether or not there is money or there are markets in the future.
My hypothesis is that the Federation's system, insofar as it can be compared to modern systems, is a mostly Socialist economy with Capitalistic sides. That is to say, the Federation has sufficient resources to ensure everyone a comfortable lifestyle of the sort we might associate with the middle class in the modern Western world; any household can have free, reasonable-sized shelter, free food, free clothes, free and excellent medical care, and free basic communications services (the 24th Century equivalent of a cell phone with a few hundred minutes per month, or of basic Internet service, etc). Education, from pre-K up to the PhD level, is free and universally excellent -- even if every school isn't Harvard, there's no such thing as a truly crappy school anymore. This is the kind of lifestyle and security that would be about what we consider the basics of doing okay in real life. I imagine the Federation and/or its Member States can provide a small stipend to all of their citizens, just for being alive.
But, I figure that anyone who wants more than all that? Needs to find a job and earn Federation credits. If you want a house that's a bit bigger, or that's located along the beach? Or if you want the latest toys, the fastest Interstellar Internet, or the most awesome hovercar? You wanna go to Harvard, or if you just generally want to have more money than your basic living stipend? Then you've got to work, or otherwise compete with others.
I also imagine that, recognizing the dangers of aristocracy, oligarchy, and plutocracy, the Federation and its Member States have strong regulations of businesses, laws against too much inherited wealth, and, possibly, not only a minimum wage but a maximum wage.
To me, that seems like a reasonable compromise between the conflicting data on Federation economics. People aren't driven by greed anymore, and life is no longer commodified and lived only at the pleasure of the marketplace. There's no more entrenched system of economic classes, and no wealthy elite is able to perpetuate itself across more than a generation or two. There's a minimum floor, a safety net that keeps people at a certain level, and there's a ceiling to keep people from becoming too powerful, too. But there's also competition, private ownership, and a requirement that those who want more have to earn it.