I think that Size vs. Quality is the classic trade-off that you can never get around. However, the reason why I brought up the subject of headphone quality in my previous post is because if you don't have decent headphones, then don't bother ripping at anything above 128bps.
For example, if I listen to my MP3 player with the $5 buds that came with it, I can't tell the difference between a track ripped at 128bps vs. the same track ripped at 256bps. But if I'm wearing a pair of my quality headphones, and/or using an external amplifier with my MP3 player - I or anyone else can clearly tell the difference.
So I think the point is: Don't rip at a high bit rate unless you have the equipment that can notice the difference. To determine the case with your Axim and the headphones you plan to use with it is very easy. Just rip your favorite track, or something you are very familiar with, at 128bps and 256bps. Then listen to each version. YOU have to be the judge - Is the improvement in sound quality worth the extra storage space?
It can also depend upon the type of music you listen to. For example, classical, accoustic, and jazz will sound better with high-detail headphones (like Etymotic) and ripped at a high bit rate to preserve the detail. For heavy metal, punk, rap, hip hop, etc. detail is not as important, and a pure rock n' roll headphone like Grados would be a better choice, and you can probably get away with lower bit-rate. There are 10s of thousands of posts debating these issues at
www.head-fi.org. There is no right or wrong answer.