For up-close portraiture, I would really look into one or more prime lenses, rather than a zoom lens. Zoom lenses are more complex, optically, and the widest aperture you can usually find for a zoom lens is f/2.8, maybe f/2. The quality you get from a zoom lens will usually be lower than what you can get from a prime, and often for a higher cost.
Prime lenses, or single focal length lenses, come with much wider apertures, as wide as f/1.2 (two and a half stops more light than an f/2.8 zoom lens, which is a lot!) You can usually find a 50mm f/1.8 prime lens for about $100 or so. Often referred to as the "nifty fifty", this lens is pretty much a must have for anyones kit. The DOF at f/1.8 is pretty thin, but not so thin that you need special skills to make the most of it. It is also possible to find 35mm, 50mm, and 85mm lenses at f/1.4. Usually more costly than the f/1.8 variants, they can usually be found for anywhere as low a few hundred dollars, and as high as a couple thousand. The depth of field at f/1.4 can be truly superb, and makes for some very nice portrait lenses.
When shooting indoors, the more light the better. Our eyes react automatically to the change in luminance between outdoor lighting and indoor lighting, so the difference (which can be considerable) is not as obvious to us. To a camera, on the other hand, the difference in light between an outdoor shot and an indoor shot can be quite large. Having an extra two stops worth of light with an f/1.4 lens will make it a lot easier to get low-noise, high quality portrait shots indoors.
Common prime lenses usually come in a standard sequence of focal lengths, and a few standard apertures. These include 24mm, 35mm, 50mm, 85mm, 135mm and 200mm (when used on a full-frame/35mm camera). Common apertures for prime lenses below 135mm include f/1.8, f/1.4, and f/1.2. Some brands may use a half-stop rather than a third-stop scale, so depending on your camera brand (or if you buy third-party lenses) you may also see f/1.7 lenses. For lenses up to 200mm, the widest apertures are usually f/2.8, or possibly f/2. Good portrait focal lengths are 50mm, 85mm, and 135mm.
It should be noted that there are few full-frame digital cameras on the market, and most DSLR's are APS-C, or cropped sensors. The effective focal lengths on a cropped sensor can generally be shifted up by one "step". For example, on a Canon entry-level or semi-pro (prosumer) DSLR, the sensor is a 1.6x crop APS-C size. A 24mm lens is effectively a 38mm on an APS-C camera. A 35mm lens is effectively 56mm lens. A 50mm lens is effectively a 75mm lens. Just multiply the actual focal length by the crop factor (1.6 for Canon, 1.5 Nikon) to determine the effective focal length. With this general rule of thumb, you can determine what focal length you need to get full-frame compatible framing. This can be helpful when reading articles or books about photography, as most of them tend to assume full-frame shooting (a lot of photography books are still based on the film world.)
Prime lenses are really great for portraiture, particularly the wider apertures and shorter DOF. They do limit you, however, in that if you need different framing/field of view, you need to change lenses to achieve it. Zoom lenses can be very convenient and are often far more versatile than a prime lens. What zoom range you need would really depend on what kind of photography you wish to do. Generally speaking, however, the same prime focal lengths that are ideal for portrait photography still stand for zoom lenses. Namely, 50mm, 85mm, and 135mm. A nice general-purpose zoom range is 24-105mm, which on an APS-C sized sensor is 38-168mm. You can usually find a decent 24-105mm f/4 lens with image stabilization for a decent price, however it would lack that wide aperture and narrow DOF. You can also find 24-70mm f/2.8 lenses (38-112mm effective on APS-C) that will give you decent DOF and great optics, but for a higher price.
What you choose will ultimately boil down to what you want to do, and how much you want to spend. Some key primes like a 35mm, 50mm and 85mm with an f/1.8 or f/1.4 aperture can be found for a decent price, and should service most of your portrait needs. They will provide the best quality, at the cost of a bit more hassle and lens changing. A quality 24-70mm f/2.8 lens will probably cost more than all three f/1.8 primes, but you will only have to deal with a single lens.
As for the 70-200mm focal length, that would effectively be about 105-300mm on a D7000. Thats a pretty narrow field of view range, and probably not really ideal for portraiture (outside of the 135mm focal length). That focal range would be great for reaching wildlife and birds, if that is something you would like to do. If your key interest is photographing family stuff indoors and outdoors, I would first recommend a few prime lenses at 35mm, 50mm, or 85mm, and second recommend the 24-70mm f/2.8 lens. I think those focal lengths will better serve your goals.
