First up, I suppose, would be the de rigeur posing stool and posing table. Neither is particularly expensive when purchased as such, but you can get 'em cheaper.
A "posing stool" is sort of a cross between a bar stool and an adjustable office chair. Well, you really don't need the round "that's what makes it a stool" seat -- the cheapest Ikea adjustable office chair that you can forget to install the backrest on is an adequate substitute. You can also go fishing for the same sort of thing at the local thrift shop. Don't worry about the casters -- you don't want them to work anyway. You can replace them with "official" feet, or you can simply muck up the works with a dab of epoxy. As long as the height adjustment works, you're golden.
That gets your subject of his/her feet, but what do they do with their hands? That's what the table is for. It doesn't need to be anything spectacular -- as long as it will bear a little bit of weight and can be adjusted to a comfortable height, it'll do. It won't normally appear in the shot; it's just a way to help the subject find a relaxed pose.
A set of boxes for your subject to put their feet up on is also a good idea -- you can often get a more natural-looking pose, even in a simple head-and-shoulders shot, if your subject has one foot up. Don't ask me why it works, it just does. It helps if the boxes can be stacked into a sort of staircase or be placed side-by-side to form a riser, that way you can also use them for full-body shots or to lift the little ones up to a comfortable working height for you. You can buy the boxes ready-made, but if you're handy with a table saw, a drill (for the interlock dowel pins) and a router or a jigsaw (for the hand holes), you can build them yourself for the price of a sheet or two of plywood.
Beyond the basics, the thrift store is your friend. A little bit of paint and some cheap throws can cover a multitude of sins. Remember, you don't need furniture that looks nice, you need furniture that looks nice in a photograph. You may have what you need already, but if you're dedicating a studio space, then there's no need to spend a lot unless you're trying to develop a luxury niche clientele. Like a Hollywood Old West town, it only needs to look good from one angle (and, of course, it needs to be safe to sit, stand, or lean on, as applicable).
