one day family xian tour and transportation

Hן
we are 3 adults( age 50-81) and 1 child age 11 that want to make the most of the little time but not in a private tour because of cost.
We will be arriving Sept 28 at 9:35am from beijing and fly out the same day at 21:25 to chengdu.
we would like to see the city attractions including the Music Fountain at Bid Wild Goose Pagoda Square at ~12:00 and after that to the Terracota Warriors, . We need a service that can take us and i assume the best way will be a taxi for the all day or 3 separate taxies - airport to city, city to terracota and terracota to airport.
how much can be the price for a full day taxi or the 3 seperate rides?
can we use the left baggage in the airport?
any other or beter suggestions?
thanks
doron