Ideally, you will need both a 3 Jaw self centering chuck, and a 4 jaw independent chuck.
Self centering chucks very rarely hold work absolutely concentric.
A good 3 Jaw should hold work withing 0.005" (0.127 mm ) But the eccentricity may vary according to the diameter being held, because it depends on the accuracy of the scroll in the chuck, and the teeth on each chuck jaw..
A 3 jaw chuck will allow you to hold, round, hexagonal or triangular work.
A 4 jaw independent chuck will allow you to hold, square, rectangular, octagonal or irregular work.
It will allow round work, or bores to be centred accurately. With a finger clock and practice, it should be possible to centre work within 0.0005" (0.012 mm )
It will allow work to be machined off centre deliberately. Not too long ago, I used a 4 jaw independent chuck to ream a hole 2.5 " (63.5 mm ) off centre.
Ideal for turning eccentrics for engine valve gear!
If chucks cannot be obtained which fit directly, it will be necessary to machine a backplate for each chuck. If suitable backplates are not available, you may need to machine both sides, (Register for the flange on the Mandrel, and then the register and face for the chuck )
Not impossible jobs, by any means.
Measure the flange on your lathe and then look at the Arc Euro catalogue to see what prefinished backplates may be available. You will still need to machine the register and face to suit the particular chuck that you have
Howard