When you host a crew, the cosmetics that were last used by your crew should automatically be equipped, if the host owns the cosmetics that were used. Either that or the cosmetics that you last equipped (no matter if someone else later replaced it with something else) should then be auto-equipped. It gets annoying having to equip everything again every time.
The same could go for pets, actually. I'd like my parrot to be with me at the inn from the start. :)
EDIT: @redeyesith proposed this as an alternative, and I think it is a better solution - "I think a better idea would be the option to save loadouts for the Ships so that if you have some designs that you like a lot they can be more quickly applied at the start of the session. Require the saves to have you at the Outpost at the same range as applying them, and let us name them as we see fit (this would sort of give the feeling of "naming your Ship" as well and since these would only be visible to the player that saved it there is less issue about needing filters and such for it)."
