used only on certain jobs.
Maybe, but if you intend to remove and re-chuck a part, the 4 jaw is by far the better choice for concentricity on remounting – if one can master the technique easily or have the time to fiddle until it is right.
So it depends… I would say start with a good 3 jaw if your needs are simple. Otherwise, you will find, as many have, that the 4 jaw independent is often the choice (mine is – because it is there ready and waiting. By the time I have changed chucks, the part is centred adequately).
As above, re historical operations – turning cylindrical items was often done between centres for best concentricity, particuarly if removing from, and refitting to, the lathe. But fallen out of use for various reasons (modern chucks are better than a worn out old 'un, no spinning drive dogs to keep away from, etc.).
I bought a 4 jaw self centering chuck, as well (for the rotary table). But I would not go out and buy another – they will only chuck properly on perfectly round bar, per eg.
Join your local Model Eng. Soc. and practise with a 4 jaw independent, if you have the opportunity or time. Hands on experience is worth far more than a forum reply.
If I now had a choice of only one chuck, it would be the 4 jaw independent variety. But that is after 20 years of tinkering.