There's generally no reason to use a separate RTC chip, unless e.g. you need to keep a sense of time while the main processor is shut down to reduce power consumption. You can code the clock yourself, as in the attachment.

If you keep time on the micro itself, then the tolerance of the micro's oscillator is important. A crystal should generally be good to within tens of ppm (about a second per day); but make sure the value of the tuning capacitors is correct, or it can be off by much more. This value will be determined from the crystal's datasheet, not the micro's; the tuning capacitors, plus the micro's input capacitance and the stray wiring capacitances, should equal the crystal's rated load capacitance.