In a nutshell, case fans are required to move air in and out of the PC case thereby keeping the PC components cooler; pushing in cool air, exhausting warm air.

There are typically two types of case fans and they are described by the fan blade design.
Air flow fans: optimised for moving a lot of air
Static pressure fans: optimised for dealing with restrictions like radiators, HDD cages etc.

You can choose to use either airflow or static pressure fans the difference in performance isn't significant.However, one can select based on how their PC configuration is.As a rule of thumb, where there is low air restriction within the case use airflow fans.

Fans come in different sizes and range from 40mm to 200mm but the choice is based on the PC case limitations. The standard sizes for most gaming cases are 120mm and 140mm in diameter and a width typically of 25mm. In some larger PC case size, it's common to see 180mm, 200mm and 230mm (diameter) fans.

When setting up your fan configuration always aim to keep 'positive' air flow meaning have more air moving into the case than moving out of the case. This doesn't necessarily mean have more intake fans as the speed of the fans dictate how much air is being moved. 'negative' air flow means you have more air exhausting the PC case than entering. Negative air pressure usually leads to more dust build up in the case as air is pulled through unfiltered vents on the case.

So in choosing your fan, check case support before purchasing.

Note though choosing a fan can be very frustrating as there are so many manufacturer. I usually go to thermalbench.com to do my comparisons.
On photo, airflow(AF) fan on left, Static Pressure (SP) on right. Note the fan blade design.

Related Post - https://www.nairaland.com/3267973/gaming-pc-what-need-know

You'll also find 3-pin fans and 4-pin fans. With the right headers equipped on the motherboard the fan can be controlled by 3-pin(dc voltage controlled) or 4-pin (PWM) controlled. The different is the degree or levels of control available to the end user.

PWM - Pulse Width Modulation uses digital square wave pulses which can have the duty cycle varied. The duty cycle ( ratio of the period the pulse is ON and when it OFF) controls the amount of voltage applied to the fan unlike the case of DC control which is 5V, 7V or 12V.

In a nutshell, PWM can offer quieter fan operation and finer control

I'd always recommend PWM fans or use a PWM fan hub (more on this in my mini ITX build)

If you’re building a new computer that is going to look as cool as it runs, browsing this list of unique PC cases is a good start. This tutorial highlights the 20 coolest PC cases you can buy in 2022.

https://www.novabach.com/20-coolest-pc-cases-you-can-buy/