Can't say what a "perfect" height is... it would probably vary for the individual, but here's a good idea that's worked for me. Whatever final height you decide on, deduct the height of a set of appropriate wheels. (then, of course, add the wheels :)
Having a bench that is capable of rolling-around for cleaning and repositioning is worth it's weight in gold... it's worked out well for me.
Bench height is clearly a personal preference, comfort and utility thing. Low benches probably work best for furniture makers whose items may run a bit taller on the bench, where higher seems to be the rule for more of us.
I've worked daily at a 36" high bench for five decades, and I haven't changed it as my height started at 5'8," up until my current stature of 5'6." As to bending over a lot, back problems haven't been part of my life, so I don't mind that at all
The five other guys in my shop are closer to your height and find my bench unusable, as do I theirs. They all have 39" high work surfaces. At that height, I can't reach for some maneuvers.
If you keep the construction modest, you can always chop legs or add material to change the height, so I wouldn't worry much about that issue. Just do what you need when you need.
Don't plan any shop too much. Prepare to be adaptable and expect to keep everything in flux. My architect pals tell me that we all adapt better to what we're given than we can effectively plan for our needs!
I like to sit for many operations that require fine and delicate hand-eye coordination, like fret dressing. When standing the bench top is around 40", but I usually have stands or jigs to hold the work piece, so it sits higher. I am 6' 2"
A rule of thumb for woodworking (and I am all thumbs so how does that apply to me? ) is wrist high for larger operations, elbow high for finer work, almost shoulder high for finest work. I am 6'2 and my bench is 36" and that is great for planing, and sawing for furniture. I have built a Moxon style vise that fits in my face vice that is a little over 6" tall making it 42" off the floor and this is just right for chopping mortices and dovetailing. Then I can sit on a 24" stool that fits under one end of the bench and the bench acts like it is quite high for guitar work. If the bench is too short, you can always make a small set of leg extensions of any height you like. As Frank says, try it all to see what works for you.
I had thought that 36" sounded low, until I measured mine. It was only 35" and that was after I'd made a new top from 5/8 planks rescued from an old vaulting horse. I'm 181cm, (5' 11"ish), and I have no problem working at that height. I initially gauged mine from the top of my engineering vice to my elbow, this was always a maxim for comfort when working at a vice when I was a fitter.
I built one of these and it's a great tool. The swivel jaws on the vise are great. Thanks to Steve Latta.
I can sit at a stool and do inlay quite comfortably, with a swivel lamp clamped close by on the bench top
itself. I used 2" oak scrap for the top and offcuts for the legs. Goes together pretty fast.
FWIW, I'm 5'10". My main repair and setup bench is 40.5". Table I do a lot of guitar construction on is 38". A cabinetmaking bench will be about 34"--it needs to be lower for planing.
This is WorkBench that I've been using for the last 6 years. Everyone has their own ideal height for working. Some prefer to stand ( like myself ) others prefer to sit. My workbench is about 30" high ... but ... the TechDeck raises it another 8" . This works fine for me.