AmigaOS 3.1 is an improvement (non cosmetic) over 3.0.
but if you want to anything reasonably worthwhile on a 1200 these days, including upgrade to 3.5 or 3.9, you will need more RAM, and preferably a faster CPU.
this means acceleration !
the minimum requirements for both OS3.5 and OS3.9 are a 32bit processor (which you have: the 68020 in the 1200) and at least 6MB of RAM (2MB of which is the Chip RAM).
it is recommended however, that you have an FPU and a faster CPU, along with at least 16MB RAM for ideal operation.
so this would be something lke an Apollo 68030 / 040 or one of the Blizzards.
the cheapest, I think is good ole eyetech (and probably others) who do the Apollo 1230MkIII - full 68030 clocked to 40MHz with an FPU, and a solitary SIMM slot that will take a 32MB SIMM, while still fitting in the DT case.
however, seeing as you have done a case hack, you have plenty of room for thermals, so might want to consider looking around for a cheap 68040.
try:
Eyetech,
Power computing's amiga site and
Analogic to name but three.