Assuming you already have a fork, spoon, knife, plates, some kind of frying pan and a basic pot of some sort, there are only 3 things that a real cook needs. This is the first. See other posts for items 2 (cutting board) and 3 (knife sharpener).
1. A cooking knife.
A knife of the chef’s variety with a wide blade, a sharp edge and generally from 6 to 10 inches long is the way to go. Mine is about 8 inches of the French variety. Every nationality has their own variation which, in the end, act in a similar fashion. The blade is generally designed to pivot on a cutting board, chopping vegetables on the way down. Naturally it can also be used to slice meats and other things which don’t lend themselves to being chopped. Buy some band aids or other bandages, expecting the inevitable to happen.
The knife I’ve used for many years has a carbon steel blade (not stainless steel), a wooden handle, has a bit of weight to it, stamped with the name Forgecraft on the blade. The cost at the time was about two or three dollars. I would recommend the same knife, except when I Google them now, the word vintage seems to be associated with them. I have a feeling they’re no longer made. Given that, here are two inexpensive knives that received good reviews and are in the 10 dollar range. The Farberware appears to have stainless steel handles and is forged. Some reviews note a tendency of this Farberware to stain or rust, especially if put in the dishwasher. So good advice for this or any good quality knife, wash and dry by hand immediately after use. The MIU is stamped stainless. In general people consider forged to be a better knife. When you consider a $2.50 knife has been all I’ve ever needed, either of these will probably literally last you a lifetime.