Landsraad, Guild, CHOAM
The politics of the first novel is not confusing, it is merely unfamiliar. Once you accept three institutions and what each of them owns, every bargain in the book becomes legible.
The Great Houses hold the land and the people. They pay troops, they hold fiefs, and they are the only part of the system that taxes actual places. They are also broke, indebted, and dependent on the money that flows from the substance pulled out of the desert. That dependence is the whole reason the Emperor can play them against each other.
The Guild holds the movement. It does not own the substance and it does not rule anybody, but it owns the ships and the shields and the schedule, and it takes a cut of every contract it carries. Its power is purely functional: without it, nothing moves and nobody profits. A House that quarrels with the Guild has quarrelled with arithmetic.
CHOAM holds the balance. It is a consortium, and its votes are apportioned in shares, which means influence can be bought and inherited. The Emperor controls it through a piece of abstention and the threat of a piece of legislation, and everyone in the room understands that the whole structure rests on those two levers being applied carefully. When they are applied carelessly, a minor Duke with a good marriage and a better army can be dismantled in a single evening.
So how does a house survive being useful? That is the question the first two novels are really asking, and it is not a question of virtue. Atreides rises by offering a solution to a problem the Emperor has, and the tragedy is that the solution is so impressive that the Emperor would rather destroy the solver than the problem. Being useful to the throne makes you a candidate for the trap; being merely useful to your own finances keeps you ordinary and alive.
The later books keep this machinery running with different parts in it, and the fourth Herbert-era novel is almost a study in how a coalition of institutions survives one man and then has to survive without him. If you read the first novel as an adventure, this is where it turns into a constitution.