Considering this is the second result on google when searching for "chinese drill press", i thought i would chime in.
I have 2 cheap drill presses, bought one for 60€ (3 pulleys, 10 gears, 500w) and got one for free (5 gears, 250 w). The one i bought always had about 1mm (50 thou) of runout, and i thought it was just the way a cheap drill is expected to be. As i got the second one however, i reconsidered as i measured about 5/100mm (2 thou) of runout on this one.
I finally got around to dislodging the chuck from my first drill (a B16 taper) which was pretty hard to get off, and the taper on it was also running very close to true, so i second that the chuck is the main problem in most cases, not the spindle or quill. I did however have about 4mm of axial movement when the spindle was "hanging loose", which was caused by the lock groove being cut at the wrong location and the upper bearing being a sliding fit. I put in a spring washer and a normal washer on top and replaced the worn bearings, which fixed the problem. I do however find it pretty funny that the chinese actually use regular ball bearings for an aplication that mostly sees axial loads. In my case it was 2 6201zz bearings.
So, when having checked the chuck, taper and bearings in the spindle, the only cause of error left is the large toleranced on the quill and headstock, which is hard to fix without nearly building a new headstock. The drill is however a pretty decent machine after having fixed the above.
Kind regards, Esben