There is also this area thats why just using trim wouldnt work

You say you are on a budget- are you handy? You could smooth the current popcorn yourself for almost no cost. Clearly any repairs should have been done prior to cabinet install but yes the cabinets can be removed the same way they went up presuming the installer used screws, just reverse the install order. If the ceiling has been painted it may be easier to scrape off the high spots and install 1/4" sheetrock.

Scraped down the popcorn ceiling, if you can. It is messy, but it can be done. Then smooth coat it. Or, as Hallett & Co. says, 1/4” Sheetrock over the popcorn. And then, leave it alone. No crown molding or anything else.

Lowering upper cabinets is going to reduce the height of the space on the countertops, make sure that doesn't cause issues. Depending on ceiling height I'd push the cabinets up or make fill-in cabinets for above. They are great for storing all the occasionally used kitchen items. Gaps aat the top of cabinets are dust catchers.

My thought was to lower the cabinet to put tongue and groove up and then put the cabinets back up with molding.

The ceiling has been painted before so I'm not sure it can be scraped. If in used 1/4 sheet rock would you just take down the cabinets, put the sheet rock up then reinstall cabinets? How do you attach the sheet rock? Should I use like a quarter round molding on top. I have realized I'm a little handy but I would pay someone to do this so it would hopefully look better than what I would do. My budget for supplies and labor would be about $1000. It is a small galley kitchen. I appreciate all the help!

That’s a reasonable budget- I could get the drywall done for $500 or so. Obviously the cost to remove and rehang cabinets would depend on how many. I see no need for moulding at the top but whatever you do keep it simple.

Before you decide to mess with a popcorn ceiling, you need to determine whether it contains asbestos. This was incredibly common with houses that were built up through the lates 70's. If you know that the popcorn material was applied after about 1980, it shouldn't be an issue. If there is any doubt about the age, take a small sample to a certified asbestos testing lab for analysis; it should cost less than $100. I used to work as an asbestos regulator, and homeowner removal of popcorn ceilings containing asbestos was one of the leading ways unsuspecting homeowneers contaminated their homes and exposed their familues to risk. I'm not saying you can't remove it yourself using proper procedures -- although I wouldn't myself -- it's messy, nasty work, and it's easy to screw up if you don't follow safety procedures. Here is an article explaining the issues: Removal of Popcorn Ceilings with Asbestos

Kristine, you have some very good advice already and I would like to add one thing, removing popcorn ceiling should always be done before any finished work is being done, even if you put a layer of drywall over it, it is still a messy job because you still have to smooth the existing ceiling to some extent to make it work... and if its asbestos, as kudzu9 already mentioned, dealing with it becomes not only harder but more complicated.

Good luck