Today, I think the biggest priority for Oseem augments is Phalanx and Refresh +2. I've listed out my priorities when these were only obtainable through dark matter companies. Since they're available as 6 augments per day, you may still want to be decisive about which armor/augments you hope to acquire.
Phalanx+ (Excluded slots come from JSE/crafted items)
PLD: Odyssean, Phalanx head/body
RUN: Herculean body/hands/legs/feet
RDM/WHM/SCH: Chironic head/body/hands/legs/feet (You could do Merlinic instead for RDM/SCH/GEO and other jobs that would /RDM).
Refresh +2 Sets: (Body omitted due to so many Refresh+ bodies in existence)
Herculean: Head/Hands/Legs/Feet (RUN+BLU really benefit from this).
Odyssean (or Valorous for more jobs): Head/Hands/Legs/Feet. (Fun for DRK+PLD)
Merlinic: Head/Hands/Legs/Feet (This is really best utilized by GEO, since BLM/SMN get Myrkr and other MP recovery options, but its your $12.95)
Chironic: Head/Hands/Legs/Feet (This makes WHM and SCH healing much easier. RDM only needs hands/legs/feet).
Merlinic: Mostly for RDM/SMN/BLM/GEO. (RDM only needs hands/legs/feet).
I think that's really it as far as "mandatory". Now for WSD:
If a cell is white and has no numbers, then the only way to get WSD+ in that slot is through Oseem's Dark Matter augments. Otherwise that cell has a color/pattern/number and WSD+ is obtainable in that slot through Ambuscade or Reforged (Artifact, Relic, Empyrean) Armor.
For example, BRD head/hands/legs/feet are blank, so those sets would need WSD+ from Oseem (if you're not farming Nyame yet). BRD Body is Pink and gets a Relic+3 WSD piece.
For example, Summoner/PLD/WHM get zero WSD pieces.
In the case of Samurai, it gets WSD+ in the body (Relic+3 and empy+3 body). At the same time, Samurai also gets WSD+ in Artifact and Ambuscade Legs!. (Thanks for the shaft, SE!)
Another example that is much more spread out is Warrior. Warrior only needs WSD+ from Oseem augments on Legs (so you can choose Valorous or Odyssean depending on which stat or WS you want to optimize for. To complete the description, WAR gets WSD in the head (Relic+3), body (Relic+3), hands (Empy+3) and feet (Sulevia Feet).
Theoretically, you can get some strong WSD+ pieces from Oseem that might beat out the Ambuscade pieces. (This is why I choose a non-solid color for Ambu pieces and a solid color for Reforged pieces).
Nyame, another point: You may have an easier time, just getting Nyame by clearing Odyssey v0 to acquire Nyame gear. Now, to unlocks the maximum augment of Rank 15, you must kill one Odyssey T3 NM at V1 or higher). This requires segments and Sheol C farming (which is tough to multi-box by itself without lots of preparation).
Hope this helps!