To practice patterns, perform kicks and punches, shadowbox, and do calisthenics, you do not need any special equipment—just desire. However, to build strength, flexibility, and endurance more quickly, you may want to purchase or build some exercise equipment. You may get by with just a few inexpensive minor pieces of equipment or you may purchase some expensive specialized equipment.
While stationed on ships while I was in the Navy, I had my gym in a bag that I carried to any available space. I used a sea bag that contained: strap-on hand and leg weights, hand grip exercisers, a jump rope, a rope and pulley with a special clamp that I could clamp onto any overhead beam so I could use it for leg stretches, some cable-pulls to use for chest and arm exercises, a small mat for floor stretches and sit-ups, a Bull Worker for chest and arm exercises, and an expandable pole to place across my shoulders for waist twists.
Many times, basic equipment may be homemade. The equipment may work just as well as purchased equipment but it will probably not be as durable. It is good to start with homemade equipment so you may evaluate whether it serves your purpose or whether you will actually use the equipment. If you find yourself using the equipment regularly, then it may be good to purchase a quality replacement.
If you want to have specialized equipment, buy it used. Rooms across the country are full of unused exercise equipment purchased with the intention of working out. Check yard sales, Goodwill stores, newspaper ads, http://www.freecycle.org, and consignment stores.