Most people visit Gran Canaria with a travel package that includes airport transfers. Given that Puerto Rico is a long way from the airport this definitely reduces arival stress and is a great option for families. However, getting to Puerto Rico yourself isn't difficult.
Don't do this. It's a long way down a busy motorway and you'll die of dehydration before you get half way.
Global bus line 91 runs every day between Gran Canaria airport and Puerto Rico and a one-way journey costs about six euros. Pay on the bus or find the desk at arrivals for a discount return ticket. You also need to factor in the cost of taxi from the bus station in the resort to your accommodation.
Line 91 operates between 06.30 in the morning and 20.30 in the evening with one bus every hour. The timetable lists times from Las Palmas so add about 20 minutes to calculate the departure time from the airport.
If line 91 isn't running then you'll need to walk under the motorway to the bus stop on the far side and wait for the next Line 1 bus: It runs all day except midnight to 04.00.
There are lots of websites that let you book your Gran Canaria taxi transfer in advance but they all seem to charge more than the taxis just outside arrivals. All you get for your extra money is a man with a sign at the arrivals gate.
Since there's always plenty of taxis at the airport we'd recommend just turning up and getting in one. Gran Canaria taxis are all metered and taxi travel is safe and reliable.
A taxi from Gran Canaria airport to Puerto Rico costs about 60 euros (20% more between 21.00 and 07.00, on Sundays and fiesta days). Locals don't tip taxi drivers but if you like your driver then a few euros will make him smile. Also ask for a card and his price for the return journey. You might get a discount.
Private pickup services in Gran Canaria are reliable but only save you a few euros at best. Large groups can save cash by booking a large vehicle rather than separate taxis. In general we say just get a taxi.