Here are my suggestions for the absolute, bare minimum supplies to get started with watercolor.
(These are not affiliate links--I haven't bothered to figure that system out yet, so they're just my legitimate recommendations.)
A Winsor & Newton Cotman set. (I have this specific one.) Even two years later it's still a great travel set, now that I've replaced a couple of the colors with ones I use more often. It also came with a tiny brush that I wouldn't recommend and that I've removed.
While I also purchased a Sennelier 5 color set, and a Holbein 12 color set, I don't recommend these because you'll also have to buy pans and a palette to hold it all in. We're going for the absolute fewest supplies to get going in this post.
A size 8 or 10 round watercolor brush. (Here's a set of natural fiber brushes on Amazon, if you want to splurge on multiple sizes.)
The main thing you want to watch for is that the brush comes to a nice point. That will allow you to paint fine lines and details, while using the side of the brush will let you make larger strokes or washes.
While my favorite brush is a Daler Rowney Aquafine Sable Round size 10 that has seen much better days, you can get started with any brush recommended for watercolor. Synthetic fiber brushes are going to be cheapest, but also hold less water than natural fibers. A blend is a great middle ground. Sable is usually considered the ideal material, but they can also be pricey. Check for bargain bins at a local supply shop to get a variety at cheaper prices.
Do yourself a favor and just get the Arches 140# cold press 100% cotton paper.
Always get 140# (or more) 100% cotton paper. I recommend cold press (has a distinct texture) for beginners as well, as I find that hot press (smooth finish) tends to get hard lines easier. Arches 100% cotton cold press is the gold standard, but you can find some other brands for less. I've tried Bee, Fabriano, Arches, Winsor & Newton, Lanaquarelle, Kilimanjaro, and Saunders Waterford, and all perform leaps and bounds better than wood pulp paper.