I plan on creating a design to run on the Ultra96-V2 board. Do I need both the Vivado and Vitis tools for this? How much do the tools cost?
Assuming you will want to write software for your Zynq UltraScale+ design running on the Ultra96-V2 then yes, you will need both Vivado and Vitis. The installer for Vitis will also install Vivado. If you plan to take the hw platform from Vivado straight into PetaLinux then you won't need Vitis.
The Xilinx Vivado ML Standard Edition is free. The Enterprise Edition, which adds tools like Model Composer, starts at $2,995. https://www.xilinx.com/products/design-tools/vivado.html#editions
Selecting the right installation was the most difficult part for me. What version? Install Vivado (that comes with Vitis) or install Vitis (that comes with Vivado). Ignore the advice to download the latest because it doesn't support Zynq, ...
Xilinx should hire an external party that reviews and simplifies the dowload section of their website.
I have now downloaded several things. Version matters, because 2020 and 2021 support different families. If you use Pynq, the toolchain version 'd better be the one used for the Pynq image you use.
Downloading Vitis (with Vivado) and Vivado (with Vitis) both worked for me. The install directory structure is different, but Vivado, Vitis and Vitis HLS all worked - and worked together - when I tested them.