I hate the obvious fact that balance is determined by how much money you put in.
So design the monetization so that it isn't that way.
Start them with a decent starter deck and an allowance of free "chips" to buy cards with. Give them enough to buy an entire deck of replacement cards for free. (Perhaps once they've finished the tutorial, or whatever.) That eliminates the starter/free-player disadvantage.
Price the cards in the shop all at the same rate, and make them *all* available for purchase. Nothing is locked away.
Sounds like all the money-making is gone, right? Nope. Players love making decks, and they hate destroying them. That first deck may have set them on a level playing field, but it'll get boring. They'll want more. And to get more, they'll have to pay. Don't make them re-buy existing cards to use in multiple decks, but make them buy cards they don't already have, or if they need more of the same card for the same deck.
This won't monetize as well as the current systems, but it's a lot better for the user and provides a more level playing field for them.
If you *really* wanted to level the field, you could let them trade in cards for other cards freely. Only adding cards would cost money. This would let them experiment freely, change when new cards came out, and generally not ever be at a disadvantage, except when it comes to time and effort. They'd have to do a lot of futzing about to trade in cards every time they wanted to experiment or update their deck. And if they had multiple decks they regularly played, it would be untenable. And thus they'd pay for convenience. And hats, or whatever visual gimmick you implement. Perhaps custom play mats or dice or whatever other pieces other players would see while playing against them.