Doing wildlife photography at night is going to be really, really difficult without a super high ISO, 3200 at least, more like you'd need 6,400. If you want a digital camera that performs well at 6,400 ISO, you're going to be spending a heck of a lot more than $500. Like, three or four times that. Same for figure skating, that is not a luminous environment. For figure skating you'd either need a photography pass, or a lens with a high focal length to make it work.
Before I start talking about focal lengths a lot, have a picture;
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loginIf you're using a lens with a long focal length (think of focal length as the zoom, the higher the focal length, the more 'zoom' it has), you're going to need high ISOs for what you want to shoot. Lenses with long focal lengths usually have a narrower aperture (a higher f/#) than lenses with a lower focal length. This is because of something called 'depth of field'. Depth of field refers to how much of the image is in focus. Depth of field is calculated by the focal length, focus distance, and the aperture. The wider the lens is open (the lower the aperture setting), the more shallow the depth of field will be, less of the image will be in focus. This effect is exaggerated by focal length. Something like 300mm at f/4.0 will have a super narrow depth of field, much more narrow than something like a 50mm lens at f/4.0. As well, the focus distance will also have an effect on the depth of field. The closer you are to something, the shallower the depth of field. The farther away you are, the wider the depth of field.
Here's something I shot at f/1.8 with a 50mm lens that was about two feet away;
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Here's something else I shot with a shallow depth of field. This was f/5.6 at 47mm, but I was about two, three inches away? When you focus on something that close, even with a higher aperture, the depth of field is going to be wicked shallow, check it out;
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Here's f/14 at 50mm, the focus was pretty far, I think I focused on where the bridge meets the abutment;
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This is f/1.8 at 50mm, with the focus set to as far as will go, set to 'infinity', which reaches the 'hyperfocal distance'. The hyperfocal distance refers to a point of focus where everything from that point onward is in focus. The narrower the aperture (higher the f/number), the farther away the point of focus where everything in focus will be. With a 50mm lens at 1.8, which is how this was shot, the hyperfocal distance will start pretty far out, but with something like 300mm at f/22, the hyperfocal distance will start closer. Anyway, here's the shot at 50mm f/1.8 set to infinity, with the hyperfocal distance causing everything from that point to be in focus;
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loginAs you can see, the distance has a really, really big impact on focus.
I don't really shoot long lenses, so I don't have a lot of examples of that.
That's a lot of words and pictures, but what I'm saying is; you're always going to be fighting with what light is available when shooting in low light situations. Figure skating will be tough, if you have a 300mm lens, unless you buy a really nice one, the widest aperture you'll get is f/5.6, you'd be far away, and you'd also need a fast autofocus, or be really awesome at manual focusing to make it work. Despite the hyperfocal distance being a factor, I doubt you'd be meeting it when doing figure skating shooting.
Concert photography is mah thang, I'm good at it.
Here's something I shot recently. This was done with film and a 50mm lens. The film was developed to 3200 ISO. If you want to get good concert shots, you'll want to get close. If you're shooting in a crowd with a long lens, you're going to have to be really creative to get good shots. If you want to shoot small venues, then get a 50mm lens, and get in close.
All is not lost! Buy used, buy used every day of the week.
KEH is a used camera retailer who pretty much sets the market for used cameras. My digital body is a Canon XTi,
it can be had for $140 from KEH. You can see
some of my
digital work here, all of it is 1600 ISO, and shot with the XTi.
Here's a 75-300mm lens for $80, and the good ol' EF 50mm 1.8,
goes for about $120.
I know some of the items I linked you to say 'BGN', which stands for 'bargain', but KEH is really good about quality. Everything I've bought from them that was listed as 'bargain', would be 'mint', 'good condition' or 'LIKE NEW!!!!!!!!!!!!!!!!!!!!!!' on eBay or Craigslist.
And, something that's important about that camera body I linked to, it has what's called a '1.6x crop factor', which means that the focal length will be multiplied by 1.6 (unless you buy a special type of lens called Canon EF-S). So the 50mm would perform like an 80mm, and the 75-300mm, is more like 120mm-480mm. The latter would be great for wildlife and nature photography. 480mm is a really high focal length, and I'm sure you'd find a lot of use for it.
I'm aware I have said a lot, and if anything's confusing or if you need something explained better.