Hi Kathy,
My vote would be for the 70-300mm, which I also own (and yes it is like the one in the link you posted).
I bought it before the 55-300mm was available, if I were buying now? - well I don't know, I haven't used one, so shouldn't comment, but I do tend hold a belief that a robust lens is better than a plastic one and that an FX lens on a DX camera is going to give better edge quality than a DX lens on a DX body and I'd rather pay the extra for that (and I'm fortunate enough to be able to).
That said, as Manfred notes, there are (many) times when 300mm, equivalent to 450mm on FX, just isn't long enough and I just bought a Nikon P510 camera, giving me an equivalent
1000mm, as I cannot justify the price of say, a 600mm (prime telephoto) lens for my D5000.
However, it is still very much a case that;
a) the wildlife needs to keep still - as Manfred delightfully puts it
b) it is slow lens, f/5.9
c) the noise performance isn't as good as the D5000/D5100, so using too high an iso is unwise (I actually limit myself to 400, where as I'll use 800, even 1600, on the D5000)
d) in turn, that means you need sunshine on the subject - and I live in the UK, so
that's not very likely!
If all those issues satisfied, it can produce good jpg results, more than equal to cropping the D5000 down to half size.
Of course, it could be argued that the lens on the P510 is even smaller, cheaper and more plasticky than any kit lens, the 55-200 or the 55-300
Hope that helps,