Freemium certainly seems to be a very successful model, but that doesn't have to mean other models are obsolete. Important to keep in mind, though, is that on mobile app stores, there's a ridiculous number of games available, and many of them are free. You need to have a plan on how to compete with free.
There different ways to handle free or freemium:
* a playable demo (limited in features or scope, like only a few levels) with a paid full version - this is the classic model, and it's a really good and honest one. The full version could be either a separate app, or unlockable in-game (through in-app purchase or entering a code).
* a full featured, ad-loaded free version and an ad-free paid version. Popular on mobile because ads are easy to do. People who don't mind the ads might never move to full, but ads can apparently bring in a lot of money. You could even do just the ad version, but some people hate them and don't mind paying for an ad-free version if they like the game.
* a limited, ad-loaded demo version. This one is a bit two-faced and feels a bit more sleazy to me; it's simultaneously a limited demo from which you hope people will upgrade to full, but you also want ad revenue from the demo, which itself is basically an ad for the full version.
* a free limited version with multiple, staged upgrades to more versions. Sleazy if you're dishonest about this up-front; it's a bait-and-switch if they expect to buy the full version and then don't get it. But if you're open about it, buying access to more levels or more worlds could be a totally reasonable way to do this.
* a free full version with in-app purchases that give in-game bonuses. This is the big one that seems to be incredibly effective (Clash of Clans, Candy Crush, Hay Day and all those other mobile games use this). Most people will just play for free, but a small group of addicts, or "whales" will be paying through to nose to fuel their addiction to your game. Ethically creepy if you really want to milk the addiction angle.
I'm sure there are other variations that I'm forgetting at the moment.