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To give you some tips for things to look into:

It's a really good idea to learn about Unity UI layout formatting. Mobile devices have a very diverse range of aspect ratios and resolutions, so you want to make sure that your interface always works, no matter what size the screen is. 

As a general thing, because you're making a simple straightforward game that's going to live or die by its gamefeel, you should definitely watch Jan Willem Nijman's talk, called "The Art of the Screenshake" for really great tips on how to make games feel more responsive to user input.

Some less visceral tips for making a game feel more professional: ease the player into and out of play. Going directly from the main menu to being in the midst of play feels abrupt; give the player a few moments to prepare to begin giving input. And when the player hits a game over state, provide some kind of transition to the score display. It's a small thing that makes a game feel 100x better.