Outside of the ever-popular base drawers over doors (which is a non-negotiable for me): in your opinion, in what order do your priorities fall in terms of needs and budget? In other words, what features are/were you willing to give up to fit into your budget?

2) soft close doors
3) dove tail joints
4) particular hinges - not sure options here, but keeping it on the list
5) plywood vs. furniture board
6) height - 36" wall cabs or 42"
7) custom look of close-together cabinets vs. non-custom that are always 3" sized options (so a possible need for fillers, etc, but less expensive overall than custom)
8) what else am I missing?

However, cabinets are something that you need to get right. I'd look for other areas to sacrafice before I'd go with sub-par cabinets. I'd postpone backsplash, go with a laminate floor (plan to do tile later), etc. to avoid sacraficing cabinets.

Priorities
1 was frameless, non-negotiable, so not sure how much that plays in. They were a little hard to find in my area, but this company reps several lines and said they could offer at least two options that were better made but in the same range as the Kraftmaid quote I got (didn't realize they stopped making frameless)
2 drawers, thanks to GW. Very excited about these. Dovetail construction as I was brought up knowing that's the best way.
3 taller uppers
4 full extension, soft close as these would be little jabs in my side every day as things slammed close

Ok to let go, easiest to hardest
1 39-42 uppers. Love the look, but even the 36 will give much more storage, and I can't trust my ceiling to be even enough for 42s
2 particular hinges. Soft close will be great, but beyond that I won't miss anything
3 custom vs 3inch increments, since my smallish kitchen ended up working well with those sizes. If I had more areas that were fixed to work around, might have been harder to give up.
4 plywood, as it seems consensus is this is better. However I have read that many prefer industrial grade particle board for frameless (which is what I will have), there are some here that provided good info on both options, and the cabinet guy doesn't usually push the upgrade for this line as it is well made. He actually used them in his house and could have upgraded for free, but chose not to.

To be determined, don't really want to give these up, though they were not in my required list. But if I have to cut (in no particular order)
1 deeper lowers/uppers on one wall
2 split top drawers in the 30 inch stacks
3 maybe deeper uppers over the hood, undecided as I haven't picked a hood for sure

Will have to evaluate
1 cost of pull out trash under sink and drawer inserts as I may be able to get them myself for less, need to see the price first

Drawers that will fit your items! You might want to measure your pots and pans, for instance.

1) frameless (hence dovetail/plywood became unnecessary so didn't have to spend on that)
2) full extension drawers and soft close doors/drawers
3) custom sized cabinets (width, height, and depth)
4) custom pullouts (recycle, steel-lined dog food, tray pullouts)
5) custom wood hood to mimic a picture I liked

and then....

6) various frou-frouey stuff like crown, fascia, appliques and corbels that most people think are too old-fashioned but that I will always totally love :-)

For quality-
-first is finish-the second thing is finish... the third thing is :)
-second is construction- how the boxes are made should be correct for the price point, don't give me an expensive pocket hole cabinet with a cute finish, as the price goes up it better be doweled then mortise and tenon at the top, don't give me a screwed together frameless cabinet at all. How are the glue joints? or are we only counting on staples? No plastic corner blocks at any price.
-I'm not interested in cute construction joints in plywood, or lock miters they don't do anything,just marketing, and more prone to failure
-doors must be glued- no pins or staples at any price

- perhaps also first is hardware- I don't care if soft close is standard, just available- I do care who makes it either Blum or Mepla/Grass glides or hinges- no Chinese drawer glides-

Plywood, particle- I don't care so long as I have options for both (especially shelves). I do care what kind it is and where it came from- give me domestic particle over Chinese ply any day of the week if the cabinet is built properly and it is a good grade. Prefer particle for frameless myself (my own kitchen) Love the option of melamine interiors.
Service and backing- I should be able to get answers today and have no hassle replacements when needed, on time delivery is a given.
Replacements should be rarely needed, wood grading should allow for reasonable color consistancy even in the middle of the road.

Design flexibility- even with middle of the road cabinets I should have a decent selection of modifications and be able to do custom sizing-it makes for better kitchens and improved storage- even my middle of the road pocket hole cabinet (compete with the box store) allows for 1/16th inch alterations- when I was looking for a doweled cabinet I had one so called custom company that offered only 1/2" changes (kidding right?)
Give me more than 3 wood choices and good colors-
as prices go up I should be able to have more choices, better premium finishes, select grades in light colored woods

Marketablity- this part of the list is for things the public thinks are important-I don't think these things are as indicative of quality as some do....
Dovetail drawers- why here and not under quality? because there are plenty of well done drawers that are not dovetail- I do want solid wood sides and good bottoms.
-good colors and styles
-soft close available
-plywood available
-framed frameless inset- I carry different brands to suit- I like frameless but can design just fine with framed especially if the mods are there
-I prefer to have the accessories available from the factory so want an adequate selection- once the price goes up I should get what I want

It's interesting to see your thoughts on plywood vs PB. I have heard/read from several places about quality concerns with plywood in recent years. One local custom shop I saw at a home show will only use a local plywood company. Says it's the best he can find anywhere, and it's consistent. (and just because people here will understand...the cabinet guy was super excited to talk about construction, materials, and "guts" as that's what he feels is important. I was the first person he recalls in a long time that wanted all the details up front...thanks GW!)

How do you find out where the PB or plywood came from? Does a custom cabinet maker really know, if he gets it from a middle man? Do the companies who sell American made cabinets to the big box stores get all of their supplies from China?

Also, how do you find out if the cabinet without dovetail is still good quality? I am waiting for a quote from a local custom guy where dovetail is an upcharge. When I asked him about that, he said dovetail is beautiful to look at, but there are advances made over the years in technology that allow for a well built drawer without the need for dovetail. That makes sense, but I just wonder if he's giving me a good pitch to not to do the work, you know?

The other thing I'm worried about going local custom is the finish. He sprays the cabinets in house and puts a strong varnish on them but he does say over time they don't wear as well as staining does. Is that typical with all paint finishes, or will I see better results from semi-custom big-box cabinet places?

Stain will always age better no matter who does it. Factory paint will be tougher. If I were having a local guy do a painted cabinet I'd seriously look into site painting them with something renewable- there was a great thread on that recently look around. I've seen plenty of old fabulous gracefully aged white kitchens that were painted on site. Otherwise I'd concentrate on which semi custom (or custom) brands are known to have good painted finishes.

Who you work with is more important than what brand you get. Find someone who has fair pricing, fits and respects your budget, that is a good personal fit, you feel you can trust, think will follow through, appears to pay attention to the details ---use them. You will end up with a better kitchen and a more pleasant experience that way.