As I was blending up a tomato soup today, I was thinking about basic tools that I, well, can live without but would rather not.
This is obviously not an exhaustive list but includes things I'd buy first if I was rebuilding a kitchen from scratch.
An immersion blender with whisk attachment. Blend, puree, whip - they generally come with a small food processor attachment too.
A thin but firm metal spatula
A fisk - or whatever tool works best for you for getting lumps out of sauces.
More rubber scrapers than you think any two households need, or at least two you really like
Microplane for zesting, grating nutmeg, and more
Bowl! This is 100% personal preference - my favorite mixing bowls are a type by Rubbermaid that aren't made anymore
(note: I get super sensitive to noises, thus the non-scraping-noises scraper and wisk-took)
French knife - ours is the 12" one my husband prefers, because he's a giant. My personal one is 5" long.
A good sharpening steel is handy
Self-healing cutting board - at least two
Good-quality 12" fry pan*
Good-quality 1-quart saucepan
Big multi-quart pot - 6-8 quarts or so
Pyrex Pans - 9x12, 9x9
A good bread pan - I like Chicago Metallic
* So these don't have to break the bank. Specialty stores often have a scratch-and-dent section or floor-model sales; All-Clad has a yearly seconds sale, and there are things like estate sales and garage sales, too. Almost all of our nice pans came from seconds or scratch-and-dent sales and they have never dented our cooking. :-) But that nice clad bottom really helps with heat management.
Pyrex liquid measures, quality metal spoons and cups with the numbers engraved - worth the investment. Believe me. Your heirs will thank you.
Get cleaning tools you like to use so you'll use them, but I cannot strongly enough recommend stainless steel scrubbers. So. Good.