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I have a Nikon D40 and a 55-200 lens. It is perfectly functional for bird photos, especially given the budget (see pic related). I haven't checked recently, but you could easily get this or maybe a better setup in good condition for under $200, maybe even under $150.
Something like a D200/300 might be a better deal, with higher resolution and compatibility with any Nikon lens (D40 doesn't have internal focus motor), albeit a little more expensive.
You can certainly get nice bird pics, and of course and lenses you buy in the future can be used on another Nikon.