Wonderful post!

I am okay investing in some cross-class crafting activities; I thoroughly enjoy the crafting mechanis FF14 has.

What would you recommend I grab as crosscraft-skills for Weaver/Alchemist/Cook?

As far as management goes in terms of healing - I love that.
I am no stranger to healing (my prefered role in most MMO's i have played) and I really like the diversity in FF14: pet healing, raw massive heals and card based healing!
I am literally trampling with excitement to get started.