Good cheap fast zooms don't exist, period. Especially not A-type or AF. Especially not over 50mm. At least, I haven't found any, and I've searched extensively.
* My cheapest good fairly-fast zooms are both M42, so no auto-aperture. (Sears-Tokina 55-135/3.5; Vivitar-Kiron Series 1 70-210/3.5.)
* My cheapest A-type zoom is slow and not exactly brilliant. (Promaster-Tamron 60-300/4-5.6.)
* My cheapest fairly good A-type zooms aren't too fast. (Sears-Samyang 70-210/4 and 80-200/4; Takumar-A 70-200/4.)
* My cheapest good AF zooms are brilliant but slow. (F35-70/3.5-4.5; FA 100-300/4.7-5.8, silver.)
I'm a cheap bastard. I've about given up searching for faster longer zooms. Maybe when I get my next inheritance -- Uncle Lou can't last forever.