There are three aspects to designing designing a propulsion system. First, a launch vehicle needs to be selected that is capable of lifting the satellite into orbit. Second, the spacecraft's propulsion system (called the Integral Propulsion Subsystem or IPS) needs to be sized. Finally, the components used in the propulsion subsystem need to be chosen.
Choosing a launch vehicle depends on many criteria, the most important of which is, "How much will it cost?" Launch vehicles are very expensive (rated in tens of millions of dollars!) and engineers will go to great lengths to simplify a satellite in order to squeeze onto a less costly one. All launch vehicles have a shroud or fairing that encloses the satellite and protects it during launch. The amount of space inside the shroud (called the envelope) controls the configuration of the spacecraft internals such as how large a propellant tank can be chosen, or whether the antenna needs to be folded up and deployed on orbit. Other things that are looked at when picking a launch vehicle includes how reliable it is (how many successful launches have been achieved) and whether or not it is produced by a U.S. or foreign company. This latter parameter is really important for U.S. military launches, but more or less irrelevant for commercial satellites.
The amount of mass a launch vehicle can lift depends on how far it has to go. The further it must go, the less mass it can take. Sometimes it is worthwhile to have the satellite's propulsion system perform part of the orbit insertion; for high altitude satellites (like those going all the way out to GEO) it is a necessity - the launch vehicle simply can't go that far! The person deciding on the launch vehicle of choice must choose one that is a little better than needed. That way, if during manufacturing the spacecraft's mass turns out bigger than planned for, it'll still fit on the launch vehicle. This extra capability is called the launch vehicle margin. Generally, if you pick a launch vehicle lifts 10-20% more mass then your satellite weighs, that's good!
At that same time that the launch vehicle is being chosen, the propulsion engineer must determine how much propellant will be needed in the satellite. For most spacecraft, both Earth orbiting and interplanetary, the propellant mass is a significant portion of the mass of the spacecraft - sometimes over half!!! Thus, the propulsion system drives a lot of decisions about what can and can't be done with the rest of the satellite.
Here's how you figure out how much propellant your spacecraft will need:
Now that you have your propellant masses, you have to find a tank big enough to store it! You want to use a propellant tank design that your company has used before in the past, because having to test a new one (called qualification) is very expensive. But it is not uncommon that you will have to test and build a new tank. Of all the propulsion system hardware, the tank is the most common item to have to redesign from scratch.
The tank is the largest item in the propulsion system, and often it is one of the largest items in the spacecraft. Thus it drives the size and shape of much of the rest of the spacecraft. It's size controls how large the bus must be, and the launch vehicle's shroud controls how big the bus can be. So when you choose a tank, you have to keep the launch vehicle's shroud envelope in mind or you'll have to use a larger (and more expensive!) launch vehicle.
Having chosen the type of thruster to be used, you need to select a particular thruster of that type. Generally, your company will have a preferred thruster to use for that application, so the selection will be trivial.
The thruster and tank are the most important parts of the propulsion system, but there are other components to be selected. These components (collectively called the feed system) include valves, filters, transducers, and the tubing (called lines) to connect them all. The feed system controls and processes the flow of propellant from the tanks to the thrusters, and measures how much propellant is in the system. The feed system rarely weighs much as a whole, and never requires much power, so it's not a major driver in designing the satellite. But it's not unimportant and no propulsion design is complete without a careful selection of these parts.
The propulsion system design isn't done until all the other subsystems have been designed. This is because as the spacecraft mass varies, the needed propellant mass will also vary. If the propellant mass grows too much, the whole propulsion system may have to be redesigned! A good engineer plans for this eventuality and has enough margin to allow for it.