So what are the generalities of different port designs? Why are some chosen vs others? How is a shelf port different from a “normal” port?
I'm not a pro designer, but have studied the physics a bit. A lot boils down to practicality. The generality is that all of the port types
function in the same way. At very low signal levels, the most important design parameter is the tuning frequency. This in turn is a function of the volume of air in the port, the overall frontal area, and the volume of the box. Two designs with the same tuning frequency will behave the same in the small-signal regime. The response curves shown by the popular modeling software are based on the small-signal model as well
This is what I refer to as the "small signal approximation." Everything is approximate, and one way of thinking about design is to take care of the simplest approximations first, then figure out how those approximations break down in real life, and refine the design accordingly. Keep doing that until you're satisfied or run out of plywood.
Where the small-signal approximation breaks down is with... drum roll... big signals. At higher signal levels, the air moving in and out in the port interacts with the edges of the openings, and can produce turbulence, which is an audible form of distortion. Making the port physically larger reduces the average air speed in the port, which reduces turbulence. Other measures help, such as smoothing the edges, which is why many ports are flared.
At very high signals and low frequencies, I've read about the air motion at the throat of the port imposing asymmetrical forces on the driver, causing cone damage. Designers have talked about symmetrical designs that avoid this.
But larger ports are also longer, for a giving tuning frequency, and end up exceeding the available space in the box. This is where the designer has to make tradeoffs, and may even scrap a design idea if they can't find the right compromise.
As for the shape and number of ports, because all ports function the same way, the main consideration is practicality. In my DIY designs, shelf ports are a way to use the off-cuts that inevitably pile up during the project, avoiding the expense of yet one more component. On the other hand, a molded tube port might reduce assembly costs in a commercial speaker. This is an example where a DIY'er might have different constraints than a commercial maker. I try to avoid building speakers with a $95 driver and $195 worth of hardware, when my gigging conditions don't require it.