Portrait photography is arguably the biggest segment in the photography industry. The majority of photography equipment tends to focus more on portrait and people photography. Lighting is one of those key bits of equipment. The kind of lighting you use can impact a lot of things and not just the results you produce.
For many photographers, a flash or a strobe is the go-to kind of light to use. Strobes have become the established type of light to use in most controlled photographic situations. For most of my career, I too used flashes and strobes for my work. However, recently, I've started to transition toward using continuous lights for most of my photography.
This is especially the case for my portrait work. The main reason is that continuous lights improve my workflow quite dramatically. With mirrorless cameras that have electronic viewfinders, you can immediately know what the exposure is before you press the shutter button. This means I can quickly make changes to both the composition and lighting without having to take lots of trial-and-error test shots.
My favorite budget light is the Neewer CB150. The price point of this light makes it highly accessible, and it produces beautiful-looking results. The front LED doesn't stick out as much as many other lights I've used up to a certain price point. This means I can use a Fresnel lens on the light and shoot with tiny apertures, despite it only being a 150-watt light.
Of course, a lot of this is down to personal preference. Both strobes and continuous lights have their respective advantages and disadvantages. Personally, I find that continuous lights offer a far better workflow, which is extremely important to me.