The old Nikon 70-300 non-VR is pretty poor, i would avoid in favor of any of the Nikon 55-200/250/300mm options. I would also avoid the sigma Tamron 50-200/250 options, and the sigma 70-300 in all incarnations. The older Tamron 70-300 without VC is poor, but the new Tamron 70-300 with VC (the same as VR) is very good.
What you wont find for that budget is a lens with a fast aperture or speeding AF but here are the "cheap" options if you want a faster aperture:
Nikon 70-200mm f/4.0 (only 1 stop faster at the long end, less at the wider end, and only 200mm).
Sigma/Tamron 70-200mm f/2.8 The Tamron has very good optical properties. there are older versions of the Sigma going cheaper 2nd hand, quality slowly drops off with the older lenses.
Nikon 80-200mm f/2.8 AF-D (and AF-S). The AF-D model is still made and sold new. Optically fantastic, build quality is much better than most newer lenses, focus is fast despite being an AF-D design.
And with regards to price, you could buy a lens like the Nikon 80-200mm f/2..8 AF-D if you buy it second hand then you can normally sell it a few years later for a similar price. I had the Nikon 80-200 AF-D, purchased forma high street shop second hand and then sold to the same shop 4 years later and I lost 35 pounds on the sale. Less than 9 quid a year is an absolute bargain!
