Time is money
If you want to experience the Dominican countryside and the big cities; then fly to Santiago. Nevertheless, be aware the trip between Santiago and Punta Cana is going to be a 6-9 hr transit depending on traffic density, time of day, availability of bus passenger space, and experience of drivers.
Time is money. Beginning at Santiago airport expect: 1 hr +- for customs clearance, acquire taxi to bus terminal(s), securing bus seating (first come first served), travel to Santo Domingo bus terminal, aquiring taxi to cross city to grab the Expreso Bavaro bus (first come first served), travel to Punta Cana, drop off at resort entrance or bus terminal.
If you do not wish this type of difficulty then fly from Phoenix to Punta Cana. It may be worth the increase.
You have to plan accordingly. Santiago - Punta Cana transit depends of ready availability and schedules of surface transportation at times of flight arrivals and departures.
Good Luck and Regards,
PJT