My only question is where do I start to make sense of all the crafting and materials that are suddenly available to me. As I opened anniversary gifts, I got all this stuff I had no idea was even in the game. What should I be paying attention to/focusing on as I climb from 30 to 60?
Crafting materials (the essenses) are worthless. You can keep a stack or two of the "pure" elements that likely aren't even available to you yet, but otherwise I would mostly ignore it. Crafting in general isn't going to do you much good until much later on. The only exception(s) is if you can find a nice mid-level core.
Unstable Molecules and Matrix's of Unbinding you should hoard. Unstable molecules are a very rare crafting ingridient in some high level crafts. Matrix's of unbinding are a "cheap" way to unbind shit later on.
As far as crafting options go, 99% of your stuff should be given to your crafter/enchanter as a "donation" to increase their level. The early-game crafts are mostly sucky. If you do want to do something with your crafter, I highly recommend using the costume slot 1-4 crafts (defensive options are better than offensive for leveling). Health on basic hit (if you basic a lot) or health on enemy defeat are very good early to mid game options.
Most people will suggest donating to Crafter -> Enchanter -> Weapon guy -> Armor Guy. (Nearly) every level of the crafter/enchanter gives a new option... the thing is, most of those options either suck or won't be useful till 60... even still, it's the best way to go.
Leveling Weapon/Armor guy is much lower priority. Armor guy sells 2 'unique' enchants, the Wealth enchant (+credit) and Joy enchant (+rare item find). Both of these are pretty bad. Wealth is good for a credit find gear, rare item find is worthless.
Leveling weapon guy will (increidlbly rarely) sell artifacts. I've gotten a Pym Shrink and a good adv. Kungfu Artifact in about 2-3 months at being max rank. Worth it? Meh, what else are you going to do.
Runes you should hoard. 99% of them you probably won't use, but a few end up being super useful. The three most useful runewords that are available almost right away:
River of Soul - Spirit management is important in this game, and this makes it a lot easier.
Seer's Brilliance - Helps with leveling very slightly... use to be better when intelligence gave +xp, probably not as useful anymore.
Ancient Grove - Great defensive option and "cheap" rune-wise. If you don't need the spirit management of River of Soul, this is your next best bet.
Costume Cores - Any core that isn't level 60 and you aren't planning on using right this second is worthless. Any core that doesn't have 2 affix's (or a double roll) is also worthless.
The chips and other assorted shit from Fortune cards can be turned in for costumes. Unless you plan on getting 90+ of them however (ie, spend money) they are pointless to hold onto. Sell them.