on what basis is the "ist" ending chosen over the "ian" ending, and vice versa?

This Q&A comes close to shedding light on these endings:

Ernesto Rocchetti from Italy writes:

I've got a question for you. Is there any rule which tells us when to use ....er and when to use .....ist at the end of a job name? For example:

painter or nutritionist

Roger Woodham replies:

There are no rules, I'm afraid, although a number of patterns emerge. Unskilled or semi-skilled job-holders are often denoted with …er, whilst those in scientific or medical professions are often designated with …ist. But there are many exceptions.

The …er suffix is very common, but so is …or. The …ist ending is also quite common, but so is …an. We also have …ant (accountant, shop assistant, civil servant, flight attendant) …man (postman, fireman, dustman, barman, draughtsman, fisherman), …ess (waitress, hostess, Headmistress) …ee (trainee, employee) and …ive (representative, machine operative), etc.

It is really a matter of learning them and knowing them. Learn them in word families .... ."