If I may offer a renter's perspective: I always rent a full house or condo, so a full kitchen is assumed. I don't really expect a fully stocked kitchen, but I want to be able to make a full breakfast and maybe a simple dinner. Below, I'll list what I consider essentials, nice to have, and not important.
Essential: Coffeemaker with filters, a good skillet (if non-stick, not scratched up please), a good cookpot with lid, decent cutlery with a cutting board, cooking utensils, eating utensils, kitchen basics (colander, can opener, cutting board, etc.), sheet pans (1 or 2), pot holders, salt and pepper.
Nice to have: Plates, bowls, silverware, glasses, cups, etc. are essential, but they don't need to be anything but basic. Just ceramic (no plastic) and clean. Good quality pots and pans are a rare but appreciated bonus. A tea kettle is nice. An electric tea kettle is awesome. Basic spices and oils (garlic powder, oregano, cooking oil). Basic bakeware. Dishwasher with 2-3 pods.
Not important: Matching sets, full compliment of spices.
Suggestion: If you have parchment paper available, your sheet pans and bakeware will last longer.