Surprisingly enough, hearthstone has been quite f2p freindly these past years. Their new model is to basically sell overpriced cosmetics for the whales and make the game as available as possible... so the whales can play the game and use their fancy signature/diamond 3d model ragnaros hero skins.
I think if you're a new player/inactive player after a long time, you can even choose a pre-built deck to play, with all the core legendaries and all.
You can also play Shadowverse if you're a weeb.
For mobile games, huh...
Never played Pokemon TCG Pocket, but Pokemon TCG Live is pretty good, in every expansion the game just gives you a bunch of tournament winning decks for free and tell you to wreck havoc. It's also pretty easy to make a homebrew deck without spending a dime (at least in my experience).
Another TCG game I like is PVZ Heroes... but if Hearthstone is considered P2W scum, then PVZ Heroes would be that up to a thousand fold lol. Still fun if you have the good cards™
If I had any other suggestion, it would basically just be "free ludo with online play", not really a big mobile fan.