After "How do I choose a curriculum?" many new homeschoolers ask "What space do I need?". Ultimately, the type of space you need will depend a lot on your personal comfort, homeschool style, age of your student(s), and the space you have available in your home.
Choosing your curriculum will dictate your space a little bit. Someone who chooses a traditional curriculum where they will spend formal class time teaching and writing examples on a whiteboard will, for example, need a space where the student(s) can sit comfortably and see the whiteboard while working along in their own textbook or taking notes. A curriculum heavy in student bookwork, like many classical styles, will need a space for the student to write comfortably. A strictly Charlotte Mason curriculum, on the other hand, needs little more than a comfy spot to read and chat.
Young students, especially those still learning self-government and the mechanics of good writing, will need the most adaptations in having a defined school space. Having a table and chair that allow them to practice good posture and the mechanics of writing will make learning to write neatly much easier. Consider here a booster seat at the kitchen table so that you can sit comfortably with your student to instruct and help keep them on track. When I was homeschooling kindergarten, we were gifted a tiny desk and chair, which was lovely to have and made Emma feel very special. It was a challenge for me, though, because the only way I could reach it was to kneel on the floor next to her!
Now that Emma is in middle school, we have bookshelves at my desk where the entire year's materials live. When I print the assignment sheet for the upcoming week, I pull out the necessary books and put them in a bin. The bin goes out near the dining room table and Emma pulls her work for a subject or a day and takes it wherever she wants or needs to. The last few weeks have been pretty solidly at the kitchen table but she also works at the desk in her room, my desk, the living room floor, the patio table, and the bed. When we have to be out of the house for an appointment, she chooses some subjects that can be easily taken in the car.
It's sometimes been tempting to spend money on classroom style decorations, charts, or big timelines. I'm always glad that I talk myself out of that, as the few times I've hung something up on the wall for us to reference, it's uniformly been forgotten about or ignored in favor of a similar resource that fits in the weekly binder with the assignment sheet and other worksheets.