Auster's Staff  

Wind Staff / Auster's Staff is used for (for RDM):

Silence - increases accuracy of spell
Gravity - increases accuracy of spell
Aero I/II/III - dmg +10% (15% for Auster's)
Aeroga (if you sub BLM) - dmg +10%/15%

POSSIBLY helps sneak & invis last longer.

Elemental staves definitely help to land enfeebles of associated elements (but enfeebling+ skill helps more). It is likely that they also help the effect last longer. As for RDM, the order I aquired mine was:

1) Dark - use to recover MP faster, use with Drain, Aspir (when subbing BLM), use with Blind
2) Ice - this is the first *must have* staff for a Red Mage - use to stick Paralyze and to MB Blizzard spells on Distortion.
3) Earth - the 2nd *must have* staff for Red Mage - you will have trouble landing Slow without this past about level 55. Also good to have if you have to be a meat-shield for some reason.
4) Wind - helps land Gravity and Silence. Silence is a must when fighting mage-type mobs. Also useful for Maat fight.
5) Light - give your Cures an extra punch, especially helpful after convert.

Those are the only staves I carry as RDM, so far. For other nukes, I either use Ice Staff or Mythic Wand. Elemental skill+ becomes much more important for nuking as the mobs get higher and higher in level in relation to you.