I have a Rivett 1020S and the Aloris BXA series quick-change tool post
and holders have been recommended to me.

I haven't worked on a lathe since high school (25 years ago) and so I
would really appreciate your recommendations on what holder 'numbers'
to start out with (e.g. #1, #2, #4, etc.).

To start out with I'll be doing a VERY slight taper (for about a length
of 1") on a 3/4" round x 2" long (when it's finished and cut) stock. I
assume that I'll drill the 1/2" center hole rather than bore it (I'm a
newbie).

Eventually I would like to make some chess pieces.

My guess is that I need the following BXA sized holders at a minimum:
#1 Turning and Facing Holder
#2 Boring, Turning and Facing Holder

But I don't know when and why I would need the #4, 41, 4D, 41D, 100,
104, 141, or 42 as an example.

The whole concept of universal tool holders (#20, 22, 30) and triangle
carbide insert holders (#12, 12N, 16, 16N, 23, 80, 80L, 15, 15L) and
knurling holders (#10, 19) is completely new to me.

Thank you for your help. Mark