cpu, ram or bandwidth -- what is most important for bitcoin mining?
CPU is basically the only thing that matters.

The memory requirements for mining are trivial (enough to run bitcoind; SHA256 uses only a few bytes of memory).  Having more that enough will add no benefit.  Disk performance is nearly irrelevant also.  

A fast network connection may help you get new blocks a little bit faster.  This is helpful because the time in between when a new block is released and when you get it is effectively wasted mining time.  But even with a very slow network connection, this should be at most a few seconds.  With a 10 minute block time, the difference between the slowest and fastest network connection should impact mining efficiency by less than 1%.