What lens to use for low light auditorium photo?

Hi, I use a nikon d40 body, and 18-55mm vr kit lens. I also use a nikon sb-400 flash. I want to take very good pictures of my kids' low light auditorium performances, specifically choir performances and some talent show, orchestra. I generally arrive at the venue early to get a good seat. Still, I know my kit lens will not get the zoom I want, and lighting/exposure will be poor. Also, I think ISO 800 is already too grainy, so I don't want to just crank up ISO. I do not mind renting a lens, but want to stick with nikon. Does anyone out there have a suggestion as to which lens I should use, and with what settings (shutter speed/ aperture combination)? Also, if I want to take indoor swim meet pictures (indoor action shots), does your pick change?

Low light stage, set ISO high, aperture priority, and use the smallest f/number of the lens. Never mind if the lens isn't long enough. You can crop the picture later in the computer. Just shoot at highest megapixel. If you will rent or buy a lens, get the lowest f/numbered lens you can afford.

For swim meets, it would be the same but if lighting is better, just decrease ISO for less grain. Using the largest aperture size (smallest f/number) assures you of the fastest shutter speed on that given situation. If the picture blurs, increase ISO.

First buy a tripod. You may get away with long shutter speeds when they are playing. However, you can also get a low aperture lens such as the 50mm f1.8.

I would recommend getting a 70-200 2.8. Nikon's version is around 2000, which I wouldn't recommend going for unless you can afford it. Third party manufacturers such as Sigma and Tamron both make a copy that runs for around 700/800 and are just as great, but lack the Nikon's included VR (Vibration Reduction).

For the stage performances, I would use my Sigma 70-200 2.8, crank my ISO to around 2500 (I have a d90, which allows me to go up to 6400 iso, but 2500 should be sufficient for stage lighting- You can always remove excessive noise in post processing from high ISO's). When in low light, always go for the lowest aperture possible first- So I'd set my camera to manual, 2.8 aperture, and experiment with what shutter speeds I can get to get a decent shot- hopefully around 1/100 of a second (you don't need much higher for non-action shots). If the shot is too dark, lower the shutter speed some (going below 1/60 second will cause some blur). If the shot is too bright, either raise the shutter speed, or lower the ISO. I wouldn't recommend using the flash in this situation unless you can get it positioned off-camera and very near the performers (your kids). Oh, also, you may have to mess around with the white balance in the auditorium a little bit, it may be hard for your camera to automatically meter the correct white balance in there.

Unfortunately, indoor swimming pools have just as bad lighting than those of auditoriums- if not worse. For this, I would recommend going with the flash, raise ISO as high as possible, drop down the aperture again, leave it on A (aperture-priority), and make sure your getting at least 1/100 shutter speeds. Try to get in a position where there's a small field of view (zoom in) or else you will see the flash disperse as the distance grows in the picture and it will probably not look the best.

Hope this helped, hit me up if you need any more help/suggestions