As with everything in photography it depends on what the subject is, what the shooting situation is and what 'quality' you want the results to achieve,..ie what size reproduction, if any.
This shot is with an FD fit 100 to 300mm Tokina zoom from the late 60's used on a NEX 3 This lens has little monetary value and could be found in charity shops and similar but is capable of surprisingly high image quality with careful use and good technique. Manual focus is fast and efficient with long focal length objecives,...that's how we all managed before auto-focus! This shot was made quickly hand-held at the full 300mm but any suport of the lens will greatly increase image quality and this is vital if large reproduction in prints is envisaged. I have discovered that the NEX 3 itself is quite capable of excellent image quality at least up to 20x16 inch exhibition prints, but careful lens use/technique is vital.
I also have a Canon FD 70 to 210 f4 zoom from the mid 1980's which should be even better than the Tokina (although larger) Most if not all of the SLR makers made 70 to 200 size zooms and these can now be had on ebay for nominal sums,..all are capable of good results and might be a good place for you to start, all you need is the lens, and adaptor, plus some support aid such as bean bag/cusion/tripod etc.
The problem I have when mounting telephoto lenses on the NEX is the NEX's petite body as mounting a long tele lens makes the set up extremely front heavy. I use a Minolta 135mm f2.8 for my medium to long telephoto, focusing is quite easy and images from the set up is good. For my long to extreme telephoto I use a Minolta 500mm f8 Mirror lens, it's quite compact for a 500mm, but it is quite challenging to use hand held and requires a monopod / tripod to get the most out of it, image quality wise it's quite good, there are some compaints that it produces donut shapped bokeh which is natural for mirror lenses, but if you dont mind that characteristic then it's quite a good lens with excellent sharpness and colour rendition.
Aside from the Vivitars, I've actually already been looking at most of the ones listed so far on ebay-Tokina, and the Minoltas. Probably the most important feature for me is that it's an m mount, I don't want to have to invest in another adapter at this time. As far as focal length, at least 200mm, although the 135mm is tempting as well since it seems to be one of the cheapest options I've found so far.