Hi John,
First of all welcome to the spectroscopy. There can be a steep learning curve at the beginning, but you are on the track and it does get easier. Once you get the hang of it then it is very rewarding, adding a whole new level to the hobby.
I wrote a BAA tutorial on using BASS with the Alpy, which can be accessed here:
https://britastro.org/downloads/10412
In section 5 on page 23 I go through calibration, covering off many of the things you have found, like a cubic fit being a good compromise. I think the strength of lines can vary from calibration lamp to calibration lamp. In the tutorial I include plots/images of calibration lamps with the lines identified from 3 different sources, which may help in the identification. I found the following 6 lines worked well, though you may find a different set works best for you.
4200.67 Ar
4764.87 Ar
5852.49 Ne
6562.85 Hα
6965.43 Ar
7272.94 Ar
BASS is very user friendly and easy to get going with, while ISIS is great at processing spectra quickly with less intervention but it has a steeper learning curve and you have to get everything setup just right. There is also DEMETRA from Shelyak, which I have not used but I understand it was created for the Alpy and should also make processing spectra more straight forward.
Best wishes,
Andy