SInce it looks like we’ll be setting up yet another kitchen, the following is mostly for me but may be useful to others. It is entirely idiosynratic. “Need” is stuff it really bothers me not to have; “want” is helpful. I’d be very interested in hearing what others would add or subtract.

Need
Pots
Small skillet (for melting butter, or if you need to brown a few mushrooms or onions)
Good skillet with lid (mine is Le Creuset Dutch oven / stoofpot, 28cm / 11″ and it’s perfect – it doesn’t have a teflon finish, but things don’t stick much and it cleans easily)
Small pot (1 liter or so)
Large heavy soup pot (I have a Le Creuset 24 cm here and a 3l aluminum one in the US; I much prefer the former)
glass baking pan (for brownies, casseroles, etc)
glass bowl (can be used as mixing bowl but also can have casseroles baked in it, also for serving popcorn or vegetables)
2nd glass or metal bowl (for mixing batter, or serving popcorn)
popcorn popper (the kind with a built-in stirrer; you can pop good popcorn in a pot but you tend to ruin the pot in the process. What can I say, we eat a lot of popcorn.)
broiling pan
roasting pan (can just be the broiling pan minus broiling top)

Utensils / appliances:
Strainer (currently I have a collapsible rubber collander, a large perforated scoop and a splatter guard / screen that can be used for straining; if I had to choose just one, it would be the collander)
soup ladle
non-melting soft spatula (the one I use most has a small bulge that keeps the spoon part off the counter)
good chef’s knife
serrated knife (for tomatoes and crusty bread – prefer a small one for the former nad a large non-pointy one for the latter, but they could be combined)
tea strainer
large cutting board
corkscrew
beer bottle opener
Wood skewers (for testing baking, also for skewering shrimp or any other small thing to be grilled)
wine stoppers (preferably with a vacuum puller thingy)
coffee maker (I only drink decaf as an occasional thing, but Ted likes to be able to have it; could be a drip one, a French press or a Keurig-type)
measuring cup (English and metric, since I’ve been known to use both)
measuring spoons (I mean, basically I need a convenient way to measure anything from 1/4 tsp to 2 cups)
plastic containers, various sizes (for leftovers, though ziploc bags substitue in a pinch
plastic wrap
aluminum foil
wooden spoon
baster
potato masher (I don’t use this or the baster often, but when you need one there are no good substitutes)

Serving / Eating
at least 4 dinner plates, pref. 6
at least 4 soup bowls, pref. 6
at least 4 water glasses, pref. 6
4 wineglasses
serving spoon
salad servers (using a regular fork and spoon doesn’t work well
sharp grater (I like the Pampered Chef ones)
silverware for 4, pref. 6
small ramekin (melting butter in the microwave, serving oil for dipping bread in, etc)
water bottles (I use these for rowing and erging, but also just while sitting around the house – I dehydrate easily)

Want:
electric kettle
smaller soup pot (I have a smaller Le Creuset Dutch oven and I use it for anything that doesn’t really need the big one)
blender (nice for things like Daiquiris or breakfast protein shakes; I can live without one but it means living without the things it makes)
small cutting board (easier to wash than the big one, if you don’t need the space
utility knife
champagne flutes
foil cutter (for wine bottles – you can use a knife but it doesn’t work that well)
jar opener (rubber)
large Dutch oven (I don’t have one but would like one big enough to roast a chicken or make large quantities of soup)
electric mixer
rolling pin (you can use a wine bottle as a substitute)
crockpot (you can use a Dutch oven as a substitute but a crockpot heats lower and more evenly)
food processor
garlic press or macerator (faster than mincing)
toaster
pizza stone (absorbs / radiates heat and evens out oven temps even when you aren’t making pizza)
glass pie dish (good for pies, layer dips and any shallow casserole)
silicone cover (for warming foods in the microwave without having them explose and make a mess)
tube pan (some cakes require one, including the Jewish Apple Cake I’ve meen making or helping make since I was tall enough to peel apples into the sink)
baking sheet (for cookies and underlying things that might overflow, though foil works for the latter; but pizza stone can stand in for one)
kitchen scale (actually I use this for yarn more than for cooking, but just now I used one to check the butter and oil for a Dutch brownie mix)
wok
roasting rack (a want rather than a need because in a pinch you can use the broiler top or else sit the turkey on top of celery stalks and onions)

It’s not unlikely that I’ll remember ten more things later and update this post.