Is there a universal standard height that people try to go for when building workbenches? Should DIY tabletops be tailor made to the height of the user and how does the ideal height of the tabletop correlate to the person?
There is a large body of information about what size furniture and tools should be. The field concerning sizing furniture to individuals and populations is called Anthropometrics and information about safety and ease of use is called Ergonomics.
If you are building your own workbench for your own use, then you should size it to yourself unless you expect others to use it. Why buy off the rack if you can get tailored for less?
Most furniture is optimized for the middle of the height distribution curve which is roughly 5'8". I got into woodworking in the first place because I am 6'4" tall and absolutely nothing fits. It's all literally 6" to short.
I used the "fall drop" rule to size my generic workshop surfaces. Just stand relaxed and let your hands fall down as if resting comfortably on a surface in front of you. It's the position you hands will just fall or drop to if you try to rest them on an imaginary surface. It gives a higher bench than the using the wrist line method above.
I suggest creating a mockup first using whatever is available and easily resized. I used a chair, a sturdy box and books of various thickness. I swapped books and fiddled with the height of the mockup until I found the most comfortable height. In my case, it was exactly 39".
You'll know it when you find your own because it just feels right.
However, shuffler is correct that different work requires different heights. The "fall drop" rule sizes a bench for use with modern power tools and precision hand tools but if you use other tools you might want a higher or lower bench e.g. heavy handsaws, chisels and planes usually require something like saw bench which is usually just under knee height.
I use a mini-bench on top of my main 39" surface if I have fiddling work like soldering.
Oh, and build yourself a custom stool and work supports at the same time. You'll be glad you did.
I don't think there is specific universal height as people aren't manufactured in a specific universal height.
Googling for "workbench height" returns many results asking the same thing: what is the best height for a workbench.
This page suggests the following method:
The page goes on to say that you should consider the type of work you'll be doing. If you're doing lots of detail work, you may want to sit (so the bench shouldn't be too low or too high to accommodate a chair). If you're standing and decide to put those foam mats down to make it more comfortable, you might want to add a half inch or so. The final suggestion is if you have the space for it, have more than one workbench.
There's no real answer to this - it depends on how tall you are, what you are using the bench for and if you are standing or sitting (and then, are you using a chair or stool?). The use for it might also play a role. Things like electrical soldering work require you to be a lot closer to the project then wood working.
The simple solution to this is to find a bench with adjustable legs. Mine is adjustable by about 16" - I started with it as high as it could go (I'm 6'), but eventually brought it down a couple inches; it's still pretty high which means I don't need to bend over to work on things. I find it comfortable like this, but you might hate it.