I made some bucket hats for my friends as gifts. I made two hats - they are reversible. What I love about the fabric used for those hats is that they are special fabrics woven in Japan called Kasuri (絣). I used the solid colour for one hat but the texture is beautiful. Sadly, the photo can't really show that off.
The first hat, one side and the other side:
The second hat, one side and the other side:
I used a free PDF pattern from Glory Allan. I really like the way he drafted this pattern. His website has DIY kits as well, which will be great for beginners. Hat making is actually not that hard.