36 inches is the number you're looking for. It will fit immediately inside the door frame, so it will be just a fraction wider than the door itself.

This is the one I have. It's great. https://www.amazon.com/gp/product/B00RJFRV1K/

I'm 6'6", in the UK our doorframe standard height is exactly that, 6'6" (199cm). I have a doorway mounted expansion bar. The major drawback is the week or so of head trauma that results from walking into the thing after first installing it, until the muscle memory duck manoeuvre becomes habitual. Technically, the drawback of an expansion bar is that I cannot really train power because I'd faceplant into the doorframe/wall above the bar. But, I can close the door without having to take it down & put it back up etc.

Expansion bar - https://www.amazon.com/Garren-Fitness-Maximiza-Pull-Screw/dp/B00RJFRV1K/ref=sxin_9_ac_d_pm?ac_md=3-1-QmV0d2VlbiAkNDAgYW5kICQ1MA%3D%3D-ac_d_pm&crid=KB18V8A80XEK&cv_ct_cx=pull+up+bar&dchild=1&keywords=pull+up+bar&pd_rd_i=B00RJFRV1K&pd_rd_r=f5d6907b-752f-4b40-a78a-fa3404461918&pd_rd_w=Xh2jr&pd_rd_wg=OGr1L&pf_rd_p=7be0d365-42b5-4a96-a2d8-6c85cad85d35&pf_rd_r=J57CPH7Y9RPJ8GC67437&psc=1&qid=1604949837&sprefix=pull%2Caps%2C273&sr=1-2-22d05c05-1231-4126-b7c4-3e7a9c0027d0

Doorframe mounted - https://www.amazon.com/Iron-Gym-Total-Upper-Workout/dp/B001EJMS6K/ref=sr_1_5?crid=KB18V8A80XEK&dchild=1&keywords=pull+up+bar&qid=1604949837&sprefix=pull%2Caps%2C273&sr=8-5
This type gives you the clearance of the doorframe/wall to do power but, you cannot close the door with it in place. It also puts all of the weight/momentum downward on the doorframe (not what they're designed to withstand) - this is the most likely of these solutions to damage/break your doorframe.

Chin-ups are fine, pull-ups are fine. With my hands gripping the bar to begin either of those, I am at rest on my knees at max scapula extension. This is fine for just those exercises. I do them with my ankles crossed behind me, floor to top and back.

Anything involving leg movement where your legs are at some point hanging freely at rest is completely out. That bar you linked goes to a max height of 88.18" - just over 7'4". For your height, you would almost certainly require a bar that is at least 8' high to be able to hang and also let your legs hang relaxed, without touching the floor.

-

TL;DR - If all you plan to be doing is pullups/chinups then a doorway mounted jobby is fine. A tower is better in that you can also do other great exercises on it (eg dips), so if you have the space for one get one. If you want to involve your core (free hanging legs) then you'll need a tower with a bar that is higher than 8' and at that point it is your ceiling's height that you need to worry about.

i've never tried doing an arm workout with my pull up bar... 🤔but then again my arms aren't very strong so i think it would be much less force on the bar than my bodyweight if i tried. for you, i have no idea what would be best! however, i do love my pull up bar. i got it off amazon and it holds my weight great https://www.amazon.com/gp/product/B00RJFRV1K/ref=ppx\_yo\_dt\_b\_search\_asin\_title?ie=UTF8&psc=1

In my opinion, that type of pullup bar is dangerous, regardless of the quality. The chance of a slight swing or bumping into something while on it are too high, then the whole thing slips off the door frame. This might be better: https://www.amazon.com/Garren-Fitness-Maximiza-Pull-Screw/dp/B00RJFRV1K/ref=sr_1_10?s=sports-and-fitness&ie=UTF8&qid=1519940260&sr=1-10&keywords=pull+up+bar