Not going to get into suggesting knives and pots and pans as others can speak better to that, and it sure gets expensive... I'm lucky to have M's grandpa's Revereware pots and some oldish knives... Below are a few more picks for beyond the basics that everyone could/should have around. W/O shelling out the reddies.
15. Pepperball. A one handed peppermill anyway. I thought the electric ones were just silly but they are actually v useful. The old Pepperball does the job fine.
16. Pommery mustard. Large grained mustard. Take your vinaigrette to the next level. The old jars had a wax sealed cork, made a huge mess to open. New jars have a plastic stopper, cleaner but not as funky. Seriously, freekin wax chunks went everywhere...
17. Lamsonsharp clam knife. A total classic. At least trrrry to open a few clams. I stick w/ mignonette sauce.
18. SeaScissors. Any sturdy kitchen shears are great, but these are made especially for cutting through lobster shells etc.
19. Steamer. This type is purpose built for asparagus but will also steam ears of corn perfectly and broccoli. May seem a bit excessive but you will buy and cook more asparagus, and enjoy it much more w this thing.
20. A steel. Must have. Really a carving set is almost essential, but everyone has knives... There are many views on sharpening technique, and even though not a huge fan generally, Gordon Ramsay demonstrates a clear, traditional way of sharpening using a steel.