The type of office furniture you buy depends on the type of work you'll be doing at home. Will you be seeing clients in your home office or interacting with them only electronically? If you'll be welcoming clients into your home office, aside from having to buy more chairs, you'll have to consider the impression that your office space makes; if not, your office furniture only has to be sturdy and comfortable, and it should suit your own taste.
Until your business starts bringing in a respectable amount of money, you don't want to spend a lot on office furniture. Measure your work area so you'll know what you have room for and examine your budget so you'll know what you can afford. While you should probably stay away from used electronics, used furniture can often be a great way to get good quality at a low price, and you could end up saving hundreds of dollars.
You'll probably need a desk to hold your computer, a comfortable chair and a place to store any paperwork related to your business (invoices, receipts, tax forms, contracts, business cards, etc.), which could be either some of the drawers in the desk or a filing cabinet if your desk is a small one without drawers. A trash can and phone with caller ID are time-savers and essential pieces of equipment. You'll also need good lighting in your workspace. Those are the basics, but as your business flourishes, you can consider sprucing up your waiting room (if you have one for clients) by hanging artwork and getting some indoor plants.