Me personally I have been awakening core units first such as Katie, Iris, Spica and I also have Bernice awakened. So that covers Healer, Duelist, archer and Heavy Armor basically the core of an army.

The rest I am awakening to branch out to other areas and get stronger duelists like My Sybilla I recently Awakened and next will be Saki and Rachel. The things is I plan to Awaken as many units as I can as I play Aigis but I am choosing who I like and will benefit my team to my needs. Other may have ideas on who you should awaken but I am sure that you may have your own style in playing and it does sound like that from the way you use Momiji and Liana.

If I where you I would be thinking what does my core awakened team lack and looks like a good heavy armor, so maybe Garrett would be your next best unit? Not only is a good Heavy Armor needed for some maps and events but being male he can be used for Male only events too.

Do you have Spica? Bashira is indeed a good unit and does pack some good DPS but Spica is also a worthy investment to get and AW and if we get good constant updates may soon leave the trading post as I hear Plat units are usually the ones to get swapped around (if they ever do this).

These are just my thought, best of luck with your awakening!!