The ESP-Dev Module is likely the most flexible board you can use for your ESP32-WROOM-32 board as it is the generic definition for an ESP32. If you have a specific development module using this chip there may be a better definition, however the specific board definitions often pre-select various settings (flash size etc) based on which chips they specifically manufacture the board with.  The generic ESP32x Dev Module allows for all of the settings to be altered so it covers all variants of the chip to our knowledge.

The ESP32-S3-WROOM-1-N16R8 board is likely best selected as the ESP32 S3 Dev Module, as this allows selection of the Flash Size (16MB), and the PSRAM type in use (which I believe is the OPI setting for Octal SPI PSRAM as shown in the datasheet).  This also allows selection of the OTG features as needed depending on which USB Mode you require.

The ESP32-S3-USB-OTG Board has a number of the settings pre-defined, hence it showing a much shorter list of options compared to the generic ESP32-S3 Dev Module.

The Partitions.bin is generated as part of the build process from the partitions.csv file, which is determined from the settings for Flash Size and Partitons selections on the Board options menu.  If this hasn't generated in the Build Folder it may indicate an error in the build which we can assist with if the build output is submitted with the settings shown at the top of the page.

I hope that is some help towards answering your questions, and the ESP32 Board Package creators will be able to give more specific advice if required: 
https://github.com/espressif/arduino-esp32