i install cabinets for a living , ive never seen cabinets 9 inches deep , even from Home Depot , the uppers should be 12 deep not including the doors , base cabinets 24 deep , 34 1/2 high before tops
if you are on a budget you may consider a facelift rather than total replacement , you can replace the doors and it will change the whole kitchen , saving money for new tops that will upgrade even more , by swapping doors ,and possibly crown molding you will save money from having someone like me charging you through the nose
if you are dead set on a total redo , then there are many factors that go into cost
size of cabinets , (uppers) , there are 30 ", 36", 42" , and a country cabinet that are 48" (tall) with various widths conforming to design, obviously the taller the upper the more the cost
material of cabinet , many types of wood , oak , hickory , cherry , maple , OR the least expensive Paint , i will bet 3 out of 5 installs i do are paint kitchens , not small either , some are 50 cabinets + and they look great and the best thing about painted cabinets is touch up is easy , dent or gouge and there is a wood crayon that literally makes it disappear
base cabinets are mostly about options , simple shelf , or rollouts , lazy susans , sheet pan racks , my advice is to forgo these and add later
tops , the price of granite has come down , (at least prior to fake pandemic) , formica is labor intensive and the cost is less but close enough to granite to get you thinking , stay away from shaker cabinets , and for a small kitchen , you may be able to get a builder grade line of cabinets that fit your stated budget , they wont be amazing but they wont be total trash either