I am looking for advice on how to choose an appropriate pair_style for a rigid linear object consisting of adjacent spheres, where each sphere has a different diameter?
That is not enough information to make a recommendation.
You can use either pair styles that use a per-atom radius and then adjust their interactions accordingly or pair styles that use point particles, but have spherical interactions with a minimum. This applies to probably more than 2/3rd of the available pair styles.
What additional information should I add in order to facilitate recommendation?
How is it done in practice?
The best approach is usually not to look at the software you want to use but survey the published literature for similar studies and look at the models and methods sections to see what was used and how suitable/accurate the results would be for your needs. Then you can look at different software packages whether they have the required potentials available. Many programs also allow tabulation, so any pairwise-additive potential can be realized that way.
You look at the potential. It usually has an attractive and a repulsive branch, some are only repulsive. The location where the repulsive force becomes significant is somewhat the “effective” radius of a potential. This is represented differently in different potentials. E.g. in LJ you have epsilon and sigma or in Morse you have the minimum and the binding energy E and the width alpha of the potential. and so on.