Square Enix released a guide on obtaining gear and cosmetics in Marvel's Avengers but it seems rather convoluted so here is a quick breakdown of the important bits.
As you probably guessed by now, Marvel's Avengers will have microtransactions. The good news is that these will be cosmetic-only, according to the game's compendium on gear and cosmetics .
Heroes on the roster will have an assortment of move sets, combos, skills, gear, heroics, unlockable outfits, emotes, takedowns, and nameplates. Those last four categories qualify as cosmetics and they will be purchasable in more than one way.
It appears that the game will be littered with a ton of currencies but the two you need to keep in mind are Units and Credits. Units can be earned through completing in-game challenges which so far sound a lot like bounties in Destiny 2 and the currency itself is reminiscent of Bright Dust.
Anyway, Units can be used to purchase some of the aforementioned eye candy from vendors. If you want to purchase cosmetics from the Marketplace, however, you will need the premium currency - Credits. You cna use them to buy cosmetics from a rotating pool of items in the aforementioned Marketplace.
Credits can also be obtained through gameplay, although it appears to be limited to Hero Challenge Cards, which is just a fancy name for a battle pass.
Each hero has a Hero Challenge Card and there are both free and premium tracks on them. It takes 1,000 Credits (around $10) to activate the premium track but the currency can be earned back by completing enough tiers on it.