Very popularly grown as an ornamental in a lot of perennial gardens, Japanese style gardens, or bamboo gardens, bamboo is actually a very useful plant that can be harvested for food, timber, or crafting. You can reduce the labor of making large timber bamboos into smaller strips that are workable for weaving by choosing bamboos with thin culms. This will allow you to just come in and thin out your bamboo plants and get to weaving as soon as possible. 

Other option is to grow larger bamboo plants that produce a lot of branches. This gives you the option to just purne out the branches and leave the culms for ornamental purposes or to harvest later for larger projects or to turn into bamboo strips for other weaving projects.

Banana plants come in a vast variety of colors and sizes. They are an excellent pick for rain gardens and areas that may flood around your home, although they can also be grown in containers if you give them plenty of water and sunlight. 

Unless you live someplace tropical or that has very mild winters, banana plants will go dormant for the winter, leaving you without fiber to weave during the cold season. One way to compensate for this is to grow plants both indoors and outdoors and simply harvest your fibers from your indoor plants during the winter and from your outdoor plants during the warm season. You can also grow a variety of perennial plants and use different weaving fibers throughout the year based on their availability.

Rushes come in many different colors, thicknesses, and sizes, but since the Blue Arrows Rush is what I have growing in my edible landscape to stabilize the edge of the duck pond, it is the one I chose for growing my own basket weaving fibers, using the duck pond water to fertilize the plants and to help them grow very quickly. 

Blue Arrows Rush is also very drought tolerant so you do not need a duck or fish pond to grow it, but it certainly helps to maximize the growth rate of the plant if it is given plenty of water and nutrition, which ducks and fish will provide. You can also grow it in tubs or planters that don't have drainage holes to give your Rush plants plenty of water without raising fish or grow them in a wetland or riparium on an aquarium.