Take all of my statements with a grain of salt, but in my experience, I was not able to run Workbench 3.0 on a set of Kickstart 3.1 ROMs. It did all sorts of weird things and wouldn't load the WorkBench.
I always did a clean install, but I'm fairly positive that WB 3.1 has an "upgrade" option when installing. Someone correct me if I'm wrong, as it's been a while since I've done an install, but I'm pretty sure it's there. As for WB 3.9, it's pretty much a prerequisite to have WB 3.1 already loaded and running as this comes on CD and requires a CD-ROM filesystem already in place to install. Not sure if it will install from 3.0, but definitely does an upgrade from 3.1.
As for backwards compatibility, there are some minor differences between 3.0 and 3.1, mostly to allow better interoperability with RTG systems and Workbench screens of more than 256 colors, and maybe some data type changes. But pretty much, if it works on 3.0, it usually will work on 3.1. I'd be more concerned about apps requiring WB 2.x and 1.x. WB 3.5 and 3.9 are nothing more than bug fixes and eye candy applications applied to the base 3.1 install, so again I wouldn't be too concerned about an app than ran on 3.1 not running on 3.9.
:-D