I'll one up the question: how about almost no-cost? I'd argue that the minimum set of items needed to make great coffee is limited to:
- A way to boil water. Most people have kettles, but a pot with a lip is fine.
- A way to grind beans. Easily the most impactful investment, but you can start with a blender if you don't have anything. The grinder is almost always where spending money--any money--really counts.
- A filter. Yes, paper towels qualify.
- A way to hold grounds and/or brewed coffee. A mason jar is sufficient.
Inexpensive method A: place your filter in a shallow-ish funnel inserted into the top of a mason jar, and then add the grounds. Boil the water, and let stand for ~45 seconds. Pour over slowly, and collect brewed coffee below.
Inexpensive method B: prepare the water and the grounds, and place both in the jar. Let stand for ~4 minutes, and then filter the grounds out as much as you can.
What's amazing is that when the coffee is high quality and fresh, it's almost difficult to screw up the end result, especially if you're new to coffee.