I would hit, in this order; Supports; Tanks; Assassins, with some work on a handful of Marksmen along the way.
Support/Tank update goals;
Tie the Income items to the role so that it no longer causes poaching issues across the game, vastly improve support income via those items.
Reduce the class' dependency on item actives, improve kits to compensate, items give better stats, cost more.
-Homogenize Mage and Enchanter, as well as Warden and Tank itemization. Items to give similar stats, but champions choose items based on what actives/passives they need, whether they want to help themselves or allies.
Example;
Luden's Echo 3200G, 90AP, 600Mana, 10% CDR, Personal damage amp passive.
Ardent Censer 3200G, 90AP, 125%Mana Regen, 10% CDR, Team damage amp passive.
Locket; 3000G, 400HP, 30Armor, 60MR, Teamwide shield that replaces any other forms of shielding for it's duration (prevents stacking).
Stoneplate 3000G, 400HP, 45 Armor, 45MR, Personal HP augment active. Grants extra resistances for being surrounded.
Support champions to work on; Sona, Nami, Janna, Soraka. Take each of their kits and give them now missing item actives. Soraka gets a long CD Cleanse + CC immunity buff, Sona gets a Redemption-like new ultimate, Nami gets a 1 shot cleanse, and so on.
Tanks to work on; Leona, Skarner, Tahm, Volibear. Leona gets a new passive she can actually use; her kit now actually provides some stat scaling from items beyond resistances. Skarner VGU, Tahm damage output reduction, Volibear VGU.
Additional work put into balancing and changing every support champion for viability for solo lane play in either mid, top or jungle.
Assassin update goal;
Make sure assassins are properly designed to require all their damage sources to blow up a full health enemy. Reduce/block access to Armor Pen beyond Lethality, possibly reduce overall damage VS better slipperiness across the board. Remove/highly diminish upfront damage granted by items actives/passives (Duskblade, Gunblade) and balance their kits accordingly.
Marksmen update goal;
Transfer a large portion of their damage from their auto attacks to their kits; make the kits sharper, better defined and unique. Either remove Crit entirely or balance crit around champion kits in a manner that rewards skillful play (Vayne hitting 3rd silver arrow, Caitlyn Headshots, Tristana Bomb) instead of directly on auto attacks.