... you could go from a Tamron 70-300 f/4-f/5.6, which is one of the best of the lower-priced lenses (about 130 UK); via the Nikkor 55-200 VR lens (180 UK); up to the Nikkor 80-200 f/2.8 (680); or the 80-400 f/4-f/5.6 (1000).... and beyond!.
Yes, smaller f-numbers are better as they mean the lenses let more light in. But that equates to heavy weight and high cost. Your wife may not want to lug around something weighing 1.3 kg (the last two expensive Nikkor lenses) when the Nikkor 55-200 weighs just 335 grams and may well be all she needs..
Thank you for your help. If I may intrude on your kindness just a little more, what is your opinion on purchasing a used lens from a reputable dealer such as B&H Photo?..
Post this in the Nikon Lens forum. You will probably get better information..
Definetely consider a vr lens... since she will probably want to slow the speed down to get more light...
Sigma lenses with EX in their name are the premium models from Sigma..
Other Sigma lenses can be pretty good, too, but EX means better construction and perhaps better glass, and usually more features..
NO problem with this. B&H are very reputable and consistently attract positive comments on this forum..
As another poster, said, a VR lens (with built-in vibration reduction, to help avoid camera shake) is a good idea in a tele lens. The Nikkor 55-200 (with VR) has a good reputation and is pretty cheap..