As for what kind of lens (2nd hand), budget 100 - 300 is good for a good DOF pic, I don't know much.
I don't even understand the many numbers you guys are fighting about.
Hmm
Essentially , to make a good decision to buy , you probably want to disregard brand for a moment , and start to look at specifically the type of lenses and the general characteristics of lens.
To aid you , you will probably want to get fast lenses with constant aperture from 1.4 to 2.8. Earlier on , these numbers has surfaced when the series of pentax lenses was shown. The down side of fast lens is that they tend to be pricier.
The next decision to make is how wide or how much narrow you want to shoot. 18mm-24mm , considered to be wide lenses. 50mm to , 70mm are considered normal to long , 200mm and beyond tele.
Lens with fixed length are known as primes , they tend to be lenses with big apertures , that produce very milky bokeh wide open.
Lens with varying lengths are known as zooms ( 11-14 Ultra wide zoom, 18-24 wide zoom , 18-50mm normal zoom , 50-200mm telezoom)
for general shooting , 17-55mm , should be good for scenery and group pictures. 200mm onwards mainly for shooting far away objects , like birds , animals .
To get shallow DoF , you can get the fast prime lenses ,but you might need to get different primes to suit difference suitable needs from wide to tele. Fast zoom lenses ( zoom lens with big apertures 2.8 ) are convinent but are very expensive and heavy.
Alternatively , you can also get a long lens around 70mm to 200mm lens with variable aperture F3.5-5.6 , you will get the shallow DoF effect when used appropriately.
Long lens with smaller apertures are generally cheaper than fast primes.
Hope that helps.
