Even if you want to display time with the seconds showing, you don't need to check the time on the RTC continiously. Once a second should be enough. You can use a timer interrupt that triggers an ISR(Interrupt Service Routine) every second to do that check for you. This will free a lot of time which your arduino can use to do other stuff.

Same goes for your button(s): you can use an External Interrupt (INT) or a Pin Change Interrupt (PCINT) for them. This way the arduino will only look at them when they are pushed (and/or released).

If you combine those two interrupts (for the clock and the button), your arduino will have a lot of spare time. This is especially hand if you later want to expand your project with more buttons and motors.