Quick performance question

Your question is a broad topic that covers many key parts of Vertica. My best understanding is, surprisingly, memory is not as important as you might think. Very consistently the experts I've spoken with report database performance is tied to the correct configuration of resource pools. Take a look at some past user comments:

https://forum.vertica.com/discussion/236836/usage-of-resource-pools

Then take a look at:
https://my.vertica.com/blog/a-method-for-vertica-workload-classificationba-p223339/

Statistics are a key part of picking an optimal query plan, thus affecting query performance and to a certain degree database performance.

https://my.vertica.com/docs/8.1.x/HTML/index.htm#Authoring/AdministratorsGuide/Statistics/CollectingDatabaseStatistics.htm?TocPath=Administrator's%20Guide|Collecting%20Database%20Statistics|_____0

There is also a the concept of query performance tuning:

https://my.vertica.com/kb/Troubleshooting-Vertica-Query-Performance-with-System-Tables/Content/BestPractices/Troubleshooting-Vertica-Query-Performance-with-System-Tables.htm

Resource pool configuration affects the pool's "query budget" which directly impacts query performance. Too small of a query budget causes queries to single-thread rather than utilize all cores.