The stuff that costs money: Necro DLC (when released) and pre-order bonuses. Pre-order bonuses include stuff like the Kerrigan wings for buying the collector's edition of Starcraft 2: Heart of the Swarm, or the probe pet for buying the collector's edition of Starcraft 2: Legacy of the Void.
Any actual gameplay-related item can be unlocked for free by hitting certain achievements, mostly in Seasons. There are no micro-transactions in-game for any items. So things like stash tabs, pets (aside from the pre-order ones), portraits, banners, etc, all can be unlocked just by playing the game.

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