Guess you didn't bother trying the ClassicWB then.
It really will do everything you need unless your planning on using your Amiga as a PC replacement.
To answer your question, the 3.1 ROM and workbench offers very little over the 3.0 - it provides very basic CD-ROM support (because it was designed for the CD32, where the ROM first appeared) and adds an Animation class to the datatypes system. All of this can be added to 3.0 with ease.
There really isn't much benifit to switching to 3.1 ROMS and higher workbench versions with an A1200, unless your going to start using it as a PC replacement. Workbench 3.0 + 3.0 ROMS + Scalos + Aminet addons really is a fantastic solution for how the majority of people will use there A1200's. I personally have no reason to upgrade, with the following being my usual tasks:
Creating cool Icons for WHDload games
Playing Amiga MODS/music formats
Creating ADF Files
Archiving Amiga files
Transfering files to and from a PC
Dpaint animations for nostalgia reasons
Viewing the occasional picture, text and HTML files
If you see yourself using the Amiga for more than this, then jump straight for OS3.9 using the methods outlined above. Even then, you'll have to start building it up in order to add all the features of a well configured WB3.0. You'll endup with a better product in the end of course, but only if you use the extra features OS3.9 offers (I personally don't) over a well configured 3.0. The file system size limit can be a genuine excuse, but remember workbench 3.0 users still have the option of SFS ,which is better than FFS in many regards.
Going from WB 3.0 to 3.1 really won't benefit you at all in general Amiga use - Scalos is by far the biggest and most useful workbench upgrade in comparison.
So my advice is, considering you'll probably be using your A1200 like I do, is build a decent WB3.0 setup. For the average user where the Amiga is not the primary computer, the higher ROMS and OS versions don't offer much at all.