I didn't read through the whole thread, but I will give what I use.... just the basics.
-small, medium and large saucepans
-small, medium and large skillets (for frying eggs, making omelets, sauteeing vegies and browning/frying meat
-One large, heavy-duty skillet/sauce pan that can be used for soup, stews/frying onion rings, french fries or chicken wings
Dutch oven (can also be used for frying), roasting pan, Crock-pot... to make roasts, soups, stews. (the roasting pan for the beef/pork roasts or whole chickens/turkeys)
wooden spoons (some people don't like using these, but they are great for -quick stirring. If you have an extra-long one, it's wonderful for mixing homemade lemonade and iced tea)
-slotted spoons (to drain off liquid from meats/vegies)
-spatulas (to lift off your grilled cheese to scraping off the excesss, when you mix a bowl of brownies)
-tongs are great to flip things over or to remove slices/pieces of meat from a pan, when they're in liquid....OR when you're frying chicken wings,onion rings, french fries, etc...easy to take out of the hot oil.
-Grater/microplane.... you'd use the grater if you wanted shred carrots, cabbage, cheese, etc. The microplane is more used for cheeses (hard cheeses, like parmesan or romano for a nice topper to topper to salads and pasta dishes) and to add lemon/orange zest to recipes
-a VERY good set of kitchen knives. I love Henkel knives... BUT, I have used inexpensive knives that do the trick..... to slicing meat or paring vegies. The key is that they are sharp. Henkel seems to stay sharp, very long.
-various sizes of mixing bowls. I love Pyrex. You can beat eggs (medium), stir/whisk dressings/sauces (small), mix batter for breads/brownies/cookies or put together salads (large).
whisk (for beating eggs!! Also, mixing a vast menagerie of sauces or soups)
-I, also set out 3-4 regular spoons, so I can taste-test, while I cook. That is so I don't have to rinse off the spoon all the time, while I'm cooking.
Small Appliances (a few are obvious)
-microwave ovens are great to thaw out meats, (BUT I tend to use the meat for soups, stews, salads--it's tends to partially cook the meat under DEFROST.) cook vegies in a snap, (BUT not on HIGH. Depending on the oven, Power Level 7 - three minutes, for two servings.) reheating, (When you want to reheat leftovers, start out at 2 minutes, Power Levl 7-8, stirring or turning over. They seems to cook very uneven), and boiling hot water for recipes or a cup o' tea.
-stick blender/immersion blender
This is great for mixing soups, while still in the pan. Also, good for pureeing vegies (potatoes for mashed or others for baby food). They are great for crushing ice and making smoothies, too. Mine came with an extra-large tumber for the task. Many have different attachments. If you choose to purhase one, look for what is practical for you.
-George Foreman indoor grill/sandwich maker.
You can various sizes. For two, I would get the larger one. You'll have the luxury of grilling, indoors! They make smaller ones that are great for melt/panini sandwiches, or a single chicken breast/fish filet. You don't have to get George Foreman as they have many off-brands. Make sure they don't have "wells."
Those are for pocket/filled sandwiches. Just look for the kind that have the grates, like on a normal grill.
-small to large-sized boards are use for slicing bread or cooked meat. (I have separate Large ones for slicing raw meat as in chicken) The smaller-medium are for vegies or fruit.
-a whisk is a good mixing tool, but there are other options. The immersion blender (mentioned above) is good for SOME things. Other than that, the hand-held mixer is great for beating eggs to batters... read the manual, and sometimes they come along with recipes. If you want to really to get professional, there is the counter-top mixer. They come with different attachments.
I think that is about it. Sorry, if I rambled on. I gained most of my experience from growing up in a cooking family, along with watching many cooking programs. In the early years; Julia Child, Martin Yan, Jeff Smith, Graham Kerr and Justin Wilson. I started watching the Food Network in 1995, even though they started in '93. Emeril Lagasse and Paula Deen really have the "enthusiasm" for cooking, which is important, I think. Robin Miller has taught me a lot when you work long hours during the week. If you like the Food Network, take notes! They also have some great cooking shows on PBS, depending on where you live.
Don't expect rainbows when making egg dishes. Julia Child couldn't get it right on the air!... it takes practice.
I also read cookbooks for tips and techniques.
I hope I helped.