Desktop vs Server
The full Ubuntu Desktop image is large but it contains everything you need to turn a Raspberry Pi into your main PC. Surf the web, watch videos, write some documents, do some shopping — whatever you like. However, because of its size it only works on the Raspberry Pi 4 models with 4GB or 8GB of RAM. The Ubuntu Server image is much smaller, you can install flavours of the Ubuntu Desktop on top of it, it gives you access to the Ubuntu CLI and by extension, all of the latest open source. Ubuntu Server works on the Raspberry Pi 2, 3 and 4.
32 bit vs 64 bit
The Raspberry Pi 2 only supports 32 bits, so that’s an easy choice. However the Raspberry Pi 3 and 4 are 64 bit boards. According to the Raspberry Pi foundation, there are limited benefits to using the 64 bit version for the Pi 3 due to the fact that it only supports 1GB of memory; however, with the Pi 4, the 64 bit version should be faster.