So PoE fits in Its totally free, You dont have to buy anything to have all the content and You are not in worse position either [although having more stash tabs helps with items management, but thats more convenience].
Also DOTA fits here and League of Legends if You take it slowly. Neverwinter is also quite friendly F2P currently from what i heard, but dont except many 'cosmetic only' F2P games, devs need to eat too
Currently playing PoE, i'm hooked. Literally nothing in the store is buy to win, (although there may be some xp boosters? All i've seen are cosmetics)
It feels like Diablo 2.5, and I'm ok with that especially by being burned by D3 in the first 2 months. My only qualm is that the item rarity is VERY similar to D3. I miss that feeling of logging on to do a quick Meph run or 2 and seeing uniques nearly every encounter