IMO it's important to start with what possible uses of knots there are, and then learn a knot for each use. I'll exclude decorative knots, because those are subjective & very diverse.

Stopper knots prevent rope from passing through a hole & keep the end from unraveling. The Overhand knot is the simplest. The Double Overhand is a very simple addition to an overhand. The Figure-8 is slightly bigger, and useful to know.

Single loop knots create a single fixed loop in a line. The Butterfly (aka Alpine Butterfly) can be tied mid-line (without access to the end) or with the end of a rope, and is two overhand knots interlocked in a particular manner.

A noose is any loop that tightens when a load is applied. I like the Scaffold Knot, it's a double overhand around the standing part of the rope. Its biggest disadvantage is it can be difficult to undo. Any fixed loop can also be made into a noose by tying it around the standing part, forming a "Running <name of fixed loop>".

Bends join the ends of two ropes. The Fisherman's knot (also has lots of other names) is two overhand knots, one with each rope, tied around the standing part of the other rope. It's strong, secure, but difficult to untie. The Double Fisherman's uses double overhands. The Butterfly Bend is a Butterfly tied as a bend, it's strong, secure, and much easier to untie. The Butterfly Bend is tied the same way the Butterfly Loop is when tying with the end.

Hitches tie a rope to a rigid object. They can attach a rope to something where you have access to an end of the object like a bollard, or where you don't like tying into a fixed ring. They can be for lengthwise pulls, or for right-angle pulls. Adjustable loops are hitches tied around the standing part of the rope. For right-angle pull, the scaffold knot works well (again). It can be tied without access to the end of an object, so it works for rings and bollards. For lengthwise pull, the rolling hitch is nice, and the Rolling Hitch Ziptie is a use of the rolling hitch which works as an adjustable loop and a binding knot.

Binding knots hold only when tied around an object. The Double-Slipped Reef Knot is a common shoelace knot. The Turquoise Turtle or "Ian's Secure Shoelace Knot" are different methods of tying a structurally identical resulting knot that's a bit more secure. Worth knowing at least one of these three, or you'll only wear slip-ons or Velcro closure shoes. Also the Rolling Hitch Ziptie is worth knowing.

There are also some systems of knots called "trucker's hitch"es, which are all ways to use loop knots as improvised pulleys with a final hitch to secure a load in place. IMO they're not independent knots. Handy to know at least one sort though in case you don't have ratchet straps or snatch blocks. The Versatackle is nice, self-locking, and tied with just Alpine Butterflies and any hitch.

So, a list of 5:

1: Overhand knot. 2: Butterfly loop (mid-line). 3: Butterfly loop (with the end). 3 (used differently): Running Butterfly. 3 (used differently): Butterfly bend. 4: Scaffold knot. 5: Rolling Hitch. 5 (used differently): Rolling Hitch Ziptie. 5 (used differently): two opposed Rolling Hitches for tying your shoelaces together works, with difficulty. 2+5: Versatackle trucker's hitch formed from two Butterfly loops and a Rolling Hitch.

All except the Rolling Hitch are based on the Overhand knot. If you're willing to add a sixth knot, pick something better to tie your shoes.