The question what damage type your caster should focus on has two sides:
The first one is covered here, but I cannot find anything about the second one.
Has anyone seen a list of damage types by spell level?
\begin{array} {|r|r|r|r|r|r|r|r|r|r|r|} \hline &0th &1st &2nd &3rd &4th &5th &6th &7th &8th &9th &total \\ \hline Acid &1 &2 &1 &3 &2 &0 &0 &1 &0 &2 &12\\ \hline Cold &2 &4 &1 &3 &3 &1 &3 &1 &0 &2 &20\\ \hline Fire &4 &5 &5 &5 &3 &2 &1 &3 &1 &2 &31\\ \hline Force &1 &1 &1 &0 &0 &3 &1 &1 &0 &0 &8\\ \hline Lightning &2 &3 &0 &5 &2 &0 &1 &1 &0 &2 &16\\ \hline Necrotic &1 &3 &0 &2 &1 &1 &3 &2 &1 &0 &14\\ \hline Poison &1 &2 &0 &0 &0 &1 &0 &1 &0 &1 &6\\ \hline Psychic &1 &2 &1 &0 &2 &0 &0 &0 &1 &1 &8\\ \hline Radiant &1 &2 &2 &3 &1 &2 &2 &0 &1 &0 &14\\ \hline Thunder &2 &4 &1 &2 &1 &1 &0 &0 &0 &1 &12\\ \hline Bludgeoning &1 &3 &3 &3 &4 &3 &2 &1 &2 &2 &24\\ \hline Slashing &0 &1 &2 &0 &0 &0 &2 &0 &0 &0 &5\\ \hline Piercing &0 &4 &2 &0 &1 &1 &1 &0 &0 &0 &9\\ \hline \end{array}
I compiled it by searching the whole spell compendium by level and damage type, and just counting the results for each combination of level and damage type. I did my best to avoid counting the SRD and PHB version of spells multiple times (I.E. Only counting Bigby's Hand and Arcane Hand as one spell). The filters I used included all official sources up through Tales From the Yawning Portal as of the compilation of this chart.
Also, this chart only takes into account what was on the D&D Beyond compendium as of 7/12/2017 and thus won't include any new entries, unearthed arcana spells, or content that is missing from the DND:Beyond spell compendium. I also put my faith entirely in the categorization in D&D:Beyond. That is, if any spell actually does deal a form of damage, but D&D:Beyond didn't categorize that spell as dealing that damage type, then it would be omitted from this chart.
Finally, some spells either have multiple damage types, or have the option to choose from a variety of damage types. In both circumstances said spell was counted for every damage type that it could possibly inflict. The one exception to this is the wish spell which, due to its ability to copy any other spell of the 8th level or lower, has been omitted entirely.
WOTC's own property allows for advanced searching by spell level and damage type.
I understand that this is not the complete answer, but the specific answer is a question of effort and not of understanding. The tool is listed that can provide the information requested.
