There is a progression system behind it all, awarding you with loot boxes every level. They are somewhat similar to Battlefield's Battlepacks, in that they contain random cosmetic goodies like skins, sprays, and voice lines. It's not really anything of much value but collectors will get a blast out of it. This is the first game I've played in a while where the progression system is simply a fun bonus, rather than something that "locks you out" of certain parts of the game until you reach an arbitrary level.
The dreaded "microtansactions" take the form of additional loot boxes, which can be purchased for real money, but I honestly never felt compelled to purchase any. As far as microtransactions go, it is pretty tame, and Blizzard has confirmed that any post-launch maps and heroes will be released completely free of charge to all owners of the game, so there's no need to worry about microtransaction heroes in the future.
So far, so good, but there are a few things about Overwatch that worry me in terms of its long-term health. I cover them a bit more in detail here, but the TL;DR is that the balance is still a bit out of whack in places. Drastic changes in the beta, like Zennyatta and Symmetra going from hero to zero, as well as Blizzard's history of over-nerfing stuff, makes me wonder how balance patches for the game will play out. There's also some other little stuff, like unlimited ammo, slow base movement speed, and being able to pick multiples of the same hero, that may cause problems down the line.
Additionally, the lack of a real singleplayer campaign will definetly be a turn-off to some: epsecially when you consider those amazing animated shorts that were released in the lead-up to its release. It's a huge missed opportunity to flesh out the story of the world, as well as pad the game with some additional content. That said, I don't think the game suffers because of it, as the multiplayer is solid and meaty enough to justify the price of admission.
These are all little nitpicks and personal preferences, more than anything. It's very clear that Blizzard has put in a herculean effort into polishing Overwatch, making sure that it feels great to play, has basically no bugs or glitches, and has a solid amount of content.
Bottom Line: Overwatch is a fast, fun, and fresh take on the class-based shooter. Blizzard has made sure its first new IP in 17 years is polished to perfection.
Recommendation: If you yearn for the days of old-school Team Fortress 2, where the game was tight, lightweight, and balanced, then Overwatch is for you.