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I do not know much at all about photography but I would like to get
better indoor portraits of my 2 girls. The lighting in my home is
terrible. I am looking for an inexpensive way to solve my lighting
problem. I would like to use plain paper background (white and or
black). Should I get a reflector? If so which one would work best?
Or is there another inexpensive alternative that could work? I have a
Nikon D60 and I have a SB800 flash (that I need to learn to use).
Indoors, other than window light, the obvious and inexpensive thing to create soft light for good portraits would be an umbrella. See
http://www.scantips.com/lights/umbrellas.html for the idea of "soft", and the idea of the how to mount it. This actual umbrella part is both good and inexpensive. Umbrellas are the one "really good thing" for portraits, very soft light.
Since that umbrella is off camera, then you need something more to put the flash there with it. It could be a Nikon SC-28 flash shoe extension cord, but this is limited to only a couple of feet (else it will tip over the stands). The umbrella beside the camera (with a near reflector on other side) will still make a very huge improvement in your lighting. Or, the Nikon AS-15 PC sync cord adapter will allow you to use a 15 foot PC sync cord, but PC sync cords are Manual flash only. Many like Manual flash, but not everyone.
The best plan is that the SB-800 works great as a remote wireless flash in TTL mode, but your D60 will require a SU-800 commander to control it. Models like D80 and D300 already have that ability, but this must be added to D60 and down. This last however will allow you to add a second flash, to have main and fill lights, for wireless remote automatic multiple flash. Not inexpensive however, but very good, in two umbrellas.
Reflectors are great, but limited. About anything white works, could be a very inexpensive 2x3 foot sheet of 1/8 inch foamboard from the craft store, or it could be purchased nylon reflector. They will all work the same. The big deal is that they must be placed in the right position, which often means either a fairly elaborate stand, or someone to hold them. And that position is less obvious since the flash is not "on" at the time (with flash). And that position is fairly limited where it can be.
Reflectors are said to be "good experience", which is because they are pretty difficult to pull it off in many cases. Good, worthwhile, but just not very easy or versatile. For example, a second flash (in a second umbrella) is much easier, much more versatile, as you can put it anywhere you want it (instead of the only place it works), and you can set the power level to any level desired, instead of only whatever it does. But the reflector is a great place to start, until you know more what you want to do. For beginning tips for using reflectors, look on Google for: One Flash Portrait.
Backgrounds: White will always come out appearing gray, unless you can put more light on it. It is farther behind subject and receives less light there, which is gray. So it needs a separate and equal light on just it, same as the subject, if you want it to appear white. Black is a little hard too, as some light will hit it, and it will appear somewhat gray too. The "invisible totally jet black" appearance requires many feet of distance behind the subject, to keep all light off of it. Or velvet cloth works much better than paper, but is not inexpensive.
A gray background is often really good, because with an extra light on it, you can make it appear light, or dark, your choice.