Setting up a home studio is a perfect thing to do. A home studio is not that hard to set up that you can start with your basic equipment.
You don't need to have all the modern equipment similar to what professional photographers own while you're starting out. Perhaps in time when you are earning more, you can gradually buy additional accessories and equipment to make your professional studio.
For background, you can buy flat sheets such as double size solid colour. Experts highly recommend the paper background in cream, grey, light blue, dark red and navy blue colour. You can hang the sheet on the wall with tacks or by installing a curtain rod. Then change them according to your preference for a particular session.
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If you already have a digital SLR camera, which is already fairly well while you are beginner. But you will also need lights. An external flash will do but if you will be focusing on shooting portraits, you will have to get an extra light fixture with a stand. Having an umbrella exclusively for photography also help specially to achieve a softer light in your pictures.
To block the natural light from the window, you can use dark colours or drapery. Other materials that can be used are black cardboard or poster board that you can tape to the glass.