These are the R packages that I use most often:
Tidyverse - the main toolbox; includes readr, ggplot2, tidyr, stringr and many others
Janitor -great for cleaning column names on import, but has other useful stuff too.
Lubridate - (part of Tidyverse) for working with date fields
Readxl - (part of Tidyverse) for importing Excel files
Tidycensus - for accessing Census data via API
Formattable -- for formatting percents and other things in RMarkdown
Stringr -- string functions
Knitr -- for knitting RMarkdown pages into HTML
kableExtra -- useful for styling tables in RMarkdown pages
ggthemes -- for styling ggplots
RMySQL - for accessing data from a MySQL server
jsonlite -- (part of Tidyverse) for bringing in JSON or exporting a dataframe to JSON