Ooo! I'll be watching for the answers to this one. My exact same question so thanks for posting!

The short answer: for 3" molding with 108" ceilings the top of the cabinet would finish at 105" nominal and wall cabinets would be 51" total height set at 54" AFF nominal.

The long answer.
Standard for bottom of wall cab to finished floor is 54". With stone counters you have about 3/4" of play there but most often 54 is used.
NOTE!! In some places inspectors measure 18" from the range to the undercabinet molding though. In every case I know of where that is the norm installers will put the undercabinet molding on after inspection but YMMV so find out.

Then if it were me I would be looking at:
How level are the floors? 54 is taken from the high spot in the run. If floors are out more than 1/2" it might be wise to adjust the base cabinet height to compensate.

Now how level are the ceilings? and is the dimension 108"?
I've seen "9 foot ceilings" that measured anywhere between 105 and 109". (Just today was speaking with an architect who was saying 9 ft ceilings- when I asked about finished hgt it turns out it will be 106 1/2 to 106 3/4 finished)

New construction you have to assume reasonably level (and pray), if they are using TGI joists all the better.
Since you are doing a remodel you can determine this ahead of time, with new construction we have to guess.
Are you changing the floor out? If so will the finished height change?
If things are out more than 1/2" over the run things get very tricky.

Inset or full overlay? If inset- many brands have a wider top rail to allow some overlap for the molding while maintaining consistant rail height. Does the brand or maker you are working with do that? For instance a 2" top rail on an inset placed at 105" with 108" ceiling ht. needs 3 1/2" of molding.

Are standard sizes important? (at this point usually not) I don't know of a standard wall cabinet that comes over 48" high. Taller cabinets mean an "increase height" or "combine cabinets" modification... or two cabinets simply stacked. With IH and (often) Combine you can usually specify and exact size. Either is better (and usually more cost effective after labor is accounted for) than just stacking two cabinets.

Molding size- really should be determined on a case by case basis. Size of room, style, how level things are, and proportions. In most cases with that ceiling height and a room large enough to go to the ceiling with cabinets I am using more 4"-6" of total molding. AND almost always using a two piece stack and usually 3 (really short mounting pc, flat(ish) vertical and crown). That starts to allow for variation in level of ceiling and floor while not letting it show too much. If things are way out you need taller molding stack than if they are close to level.

I will only specify a single piece molding if the client really wants it AND the installer agrees ahead of time. Over 90" total height you not miss a couple of inches in storage height. You will notice a bad molding job...forever.

If the room itself is crowned? Will it match the cabinet molding? Or not? IF different, then: plynth blocks will be needed and the relationship of the moldings to each other must be accounted for.

That was a great answer that left me shaking. LOL

Where do I check if there is a code for cabinet height? I searched the City ordinances but couldn't find any - so far.

There was a discussion here the other day that cabinets are set anywhere between 14" and 18" above the counter, so there may not be a code?

My current counter is 36.5" high. I am pretty tall but I want them a bit lower, like 36". The current distance from the counter to the lower lip of the cabinet is 17.5" and I *hate* it. I want wither full 18", so I can fit my blender or 16", so I can reach the back of the second shelf.

The molding is not 3", it is between 4" and 5". But it is my understanding that the gap should be ~3" as the molding will somewhat overlap with the cabinet.

The questions you've listed are not to be answered here but to be directed to my contractor, right?

I cannot ask "my contractor" as I don't have one. I need to somewhat finalize my design before I can ask for an informed estimate.

However, if I understood you correctly, this is the detail that I can leave vague for now, right? Most likely, I will order the cabinets online (Bakers, maybe?), but I have to ask the (future) installer to give me the exact specs, correct?

Could you recommend a good place to read about cabinet design?

Thank you!

eleena....could you please post a link to the baker site? I am also looking to purchase cabinets online and hadn't heard of that site. Thanks!!

It's Barker Cabinets, not Baker.

There is nothing specifically in the code. If the inspector checks they use the range mfg spec which will be 18". That is ask the inspector or an installer, some places it is a non issue, others a headache.
All the rest would be dealt with prior to ordering the cabinets, during design. As a KD they would be my problem.
Learning- this forum for overall design. Details are harder, don't know of a book so again this forum. Just be diligent, same as I would have to be. Draw the entire stack, floor to ceiling to scale, in detail, showing all reveals so you know for sure it fits. (I do for every single job)