Frank Herbert never really developed the economic model of the Imperium. On some levels, it appears to be a managed economy--for example, the Emperor decides who is responsible for certain fiefdoms that produce certain goods. This is the entire basis of the plot of Dune--that the Harkonnen governorship of Arrakis is being converted into an Atreides fiefdom at the Emperor's will, with the Harkonnen thus being given a motive to try to take it back by force with the Emperor's covert assistance. Having then conquered Arrakis, the Harkonnens were to have actually held the fiefdom going forward, not just a governorship.
CHOAM appears to be the only actual corporation, and it's basically a state-run enterprise. The Emperor, along with the Landsraad, determines who gets directorships, and the directors presumably determine what the CHOAM's vast enterprises will actually do. These directors are also always lords of the Great Houses, except that the Spacing Guild and the Bene Gesserit also appear to have seats. All legal commerce appears to be mediated at some level by CHOAM.
The Spacing Guild also has some degree of say, in as much as they could refuse to carry certain goods, or choose to interdict an entire system for what it deems misbehaviour. The Emperor and the Landsraad would presumably be a check on an abuse of this power, and thus we get a hint of the unstable political tripod talked about early on in the series.
It's never made clear if the Solari is a purely "paper" currency, or is commodity-backed (e.g. by spice)--that is, is spice essentially an alternate "hard" currency, or is the Solari itself a hard currency backed by spice, in the Corrino Imperium.
The Corrino Imperium has some kind of credit system, but we know that only by implication, in that the Atreides Imperium abolishes it and declares "cash on the barrelhead" as the only medium of exchange (Dune Messiah and God Emperor of Dune both reference this), to emphaisize Imperial authority. God Emperor of Dune also explicitly states that the economy of that era is strictly spice-currency based: "The only coinage bore a likeness of Leto's cowled face: the God Emperor. But it was all based on the spice, a substance whose value, though enormous, kept increasing."
Vaguer still is the economy of the Famine Times and the post-Imperium years of Heretics of Dune and Chapterhouse: Dune. Even with Tleilaxu tank-grown spice, it's still a relatively rare commodity, and there's definitely an implication that it's still used as a medium of exchange, but the central authority is gone. In addition, the Scattering has no spice at all. While it's clear that there is an economy, its basis is left unspecified.