For beginners, I'd dig through the Google Play Store, because the common free apps there are usually well-rated. Check out the screenshots and reviews carefully - lots of users write directly about how annoying the ads are. What matters is that the app has a tutorial mode or explanatory hints so you actually understand the rules and don't just click around blindly.
Offline functionality is standard on most Sudoku apps, you'll get that everywhere. What sets you apart from the annoying versions isn't so much the features as the balance between free and not cluttered with ads. Some apps have premium versions without ads for a few euros - that can be worth it if you're planning to play regularly. Just try two or three apps before you settle on one. After a few days you'll quickly notice which one bugs you and which doesn't.