Upgrade that RAM. 256Megs is too little even for Tiger. I bought that exact Mini brand new when it first was released and even with 10.3 Panther the 256Megs RAM with 3 applications running caused iTunes to skip as it was running out of RAM and swapping to the hard drive. At the time just upgrading to 512Megs made it work great and no more issues.
That 1.25Ghz G4 Mini uses one PC2700 DDR DIM. The Full Sized desktop DIM and not a SoDimm.
It can take a 1GB Dim. I can link you to a video on how to disassemble the Mini and install the RAM.
After the upgrade, it will run 10.5 Leopard pretty well, but personally I like Tiger on that first gen Mini.