I've looked into TKD after shopping around at different styles. It seems to click better me from punches, stances, to poomsae. Dispite similar origins and similarities in style and technique I'd favor TKD to Shotokan.
I have some limitations with flexibility at the hip. Front, back and low kicks are ok. I'm otherwise fit.
There seems to be some mentions of "Combat TKD", Pre-Olympic TKD and "Traditional TKD". Would any of these, or some other style/school of TKD have adaptations towards lower (chest/waist high) kicks? For example, several schools of Karate have variations in technique and philosophy.
If you genuinely have permanent hip injuries, or anatomy issues, I suggest giving Shotokan another look (this is coming from a mainly TKD guy). If you are simply like the majority of people and stiff, and needing to work on flexibility, TKD can be a great choice.
What is your endgame? Do you just want to workout or do you see real competition in your future? It matters when making a choice of schools.
I know this will get a lot of pushback, but I will say it anyway. Yes, there are distinct differences in how different styles of TKD teach, but at the end of the day, it is still the same techniques and material. The only real difference is in the 'how' of techniques, history, and some philosophical ideas.
Since they are well documented and easy to find for research, I will not dive deep into the Kwan's other than to say they really are the most identifiable origination of TKD, for many reasons. You will find inferences to material practiced for thousands of years but beyond it being practiced in the region now called Korea, it is very difficult to solidly say it ties to modern TKD (<100-years old).
In the early days of TKD there were several Kwan's (schools) mainly established based on location and instructor availability. There is quite a lot of speculation as to where/how the material taught was really created, but there is no ignoring the fact that Korea had Major influence from occupation by both Japan and China. It wasn't exactly an easy country to reach by other than water so what knowledge was self-taught was/is heavily engrained.
A study of the Kwan's is well worth it if you want a more immersive experience to your training.
To your query, it doesn't matter. What matters is which school(s) are close enough for you to realistically workout 3+ times/week, is within your budget, and teaches a quality curriculum. The latter is somewhat predicated on what you want from your training. In reality, all the 'types' of TKD you mentioned are simply buzz words used for advertising for the most part. The exception May be Combat TKD, but only if you truly plan to compete in the league or just really want to train hard. I suppose you could compare it to CrossFit. That said, Many schools that have little to none of the descriptors you mentioned will give you a hard workout.
In my mind 'Pre-Olympic' and 'traditional' TKD are going to be similar. The defining difference will be the form set(s) they use, technical differences in the same techniques, and how/when/where they use their punches.
To help with your assessment, I suggest you take a modular approach. Think about what you want. In a gross viewpoint, you could think of it as physical exercise, competition, and self defense. Yes, there is a good amount of overlap but knowing what you want matters.