I'm about 8 levels into Egypt right now, which is the first world, and I haven't found the need to pay for anything yet.
The content trickle is interesting: After every other level or so, you get a new plant, and there are even other "locked" plants behind areas that require keys, which seem to be random drops during levels.
The kinds of mini-games they have are great. One of which was a match 2, where you flip stone slabs and match the symbols behind them, which was a nice change of pace.
Coins can be used to buy more plant food, which temporarily beef up plants (i.e. using plant food on flowers automatically gets you a lot of sun in a short burst, using plant food on pea shooters will temporarily turn it into a rapid firing pea shooter for a short time) but this is not necessary given that some flashing zombies actually give you 1 plant food. You can also buy touch powerups, that enable you to either zap, pinch, or flick zombies away, but they're too overpriced to use IMO.
So far, I'm able to use all the knowledge I've gained from playing the original PvZ to get through the levels. It'll be interesting to see what the other levels offer.