Hi
I started out with the nikon 70-300mm vr which served me well , its a nice lens to carry, has a decent zoom range, maybe if birds are your thing 300 would be a tad short... Optically its good,nice and sharp from 70-280 ish 300mm at 5.6 is a bit soft but at f8 it does the job. For the price it is a fine lens,so i would highly recommend it over the 55-200!..... Ah, i just read your budget! Maybe it would be worth saving a bit longer to get !
All the best
Phil