Good paints are really worth it, and a little bit goes a long way, but buying all your paints at once can get expensive. I'd recommend quinacridone rose, hansa yellow medium, and phthalo blue green shade, and phthalo green blue shade. This is the most economical way to get a full gamut of colors. These four colors all work very well together and can make vibrant mixes all around the color wheel. If you need a stop-sign red, just mix the rose with a little yellow. If you need a realistic green, mix yellow and the green with a little rose to make it look more natural.
If I had to add a few more colors they would be neutral tint, ultramarine blue, transparent pyrole orange, new gamboge, burnt sienna, raw sienna, and cerulean chromium.
You can get some relatively inexpensive watercolour paper and paints and give it a go. Find some youtube videos to get you started on different techniques.
But also be aware that watercolour painting is a subset of art in general. If you don't know anything about line, value, shape, perspective, rendering, drawing people and things, composition and layout, etc, you're unlikely to suddenly develop that by playing with watercolour paints.
That doesn't mean you can't play with watercolour paints, but if you haven't been interested in drawing with a pencil you're unlikely to suddenly develop a mastery of the basics while also learning a water based media, so manage expectations.
So unlike the other person who replied, I wouldn't recommend investing heavily at the outset. You can get a sakura koi field kit for $30 (and use what colors are in there) and a canson watercolor paper pad for pretty cheap and go to town seeing if its something you enjoy, before spending a lot of money on paint tubes you might never use if you find it not to your liking.
Like anything art, the primary thing that determines skill is how much effort you put into practicing and developing that skill. Start with the goal of enjoying yourself rather than imagining turning out masterpieces like miyazaki.
