I use a 125mm self centering TOS 4- Jaw chuck in the lathe. Theoretically, a 3 jaw chuck should be better than a 4 jaw for round bar. In my case the 4 jaw TOS has better run out than the 3 Jaw chuck supplied with the lathe, both are more than good enough for a hobby lathe.
Given the 4-jaw will hold square and elliptical stock, I only use the 3-jaw for hex bar now.
So how do I go about setting up chucks?
Aside from stripping and cleaning my process has been.
1. Pop mark a point on the spindle.
2. Fit a backplate, pop mark to align alongside the mark on the spindle
3. Turn the backplate in-situ to reset the register faces for the chuck.
4. Mount the chuck and pop mark to align with the pop mark on the back plate.
This should produce the very best alignment in terms of run out, and everytime you take the chuck off the machine, you can put it back exactly where it came from. Similarly, if you need to strip the chuck, the backplate can always go back exactly where it came from.
Issues – if the backplate is already 'a fit' with the chuck, you have to lose some of the meat out of the backplate, but this has not caused any noticeable problems. For the four jaw, the spigot on the new backplate was a bigger diameter than the chuck register, so perfect for this treatment
Final point – to get best run out keep everything scrupulously clean when assembling chuck to backplate, chuck to lathe, chuck jaws. Any trapped bit of swarf has the ability to throw out the alignment. Same with machined tapers, if the socket isn't clean a bit of detritis gets trapped between the taper and socket, again there is the potential for upsetting the alignment and increasing the run out. Problem is, it tends only to be noticeable when its bad, when it's tiny, it's usually found when the job didn't turn (pardon the pun) out to spec.
Bear in mind I am an expert in these matters – I've nearly finished my third engine… Feedback is a gift 
Happy Christmas
Steve