Gran Canaria is bigger than you actually think and the nicest spots are far away from the main Hotel cities, like Maspalomas and Las Palmas. So if you want to move around, there are several options for everyone.

Transport from Airport to Hotel/AirBnb

Usually your Hotel already offers a pick up from the Airport, if not you can go by bus to Las Palmas (Line 60 and 91) and to Maspalomas (Line 66), there are also other busses going further in the south. This is the cheapest way to get to your place, but takes a bit longer. Those busses are only going between 6am and 8pm approx, so if you arrive very late in the evening as i did, you need to find another way. You can take a taxi, which is very expensive or make a deal with a local shuttle bus company, which can be quite cheap. I booked a Transfer with hoppa which was 16 euros both ways and worked totally fine. The bus was a bit late on return, but all in all they do not stop as often as the local busses and they are never that full either.

Bus

Within Maspalomas and Las Palmas it's best to walk around, although it's quite big distances. If you want to go from one end to another, you should take the bus though, since parking lots are not easy to find either.

With the local global bus you can also easily travel around the whole Island. You can easily go to Puerte de Mogan and Puerto Rico from Maspalomas, as well to Las Palmas. Here's the timetable. If you plan to travel every day, you can maybe get some discount with a card, otherwise you pay for every journey.

Car

If you want to go up in the mountains or are more people, you should definitly rent a car. This gives you so much more flexibility and you can go anywhere you like, since the busses are not driving up in the very natural mountains. Also you can do your food shopping more easily. There is a lidl located in Maspalomas as well, and i had quite problems to carry around my food. You can rent a car directly from the airport, which saves a lot of time and effort, or rent it in a local place, where it is also possible to only take them for one or two days. If you want to make a reservation online, most places only rent them for a full week.

Motorbike/Bike/Scooter

You can rent motorbikes, bikes and scooters in local places around Maspalomas. A bike can be quite useful to get around in Maspalomas, but still it is very steep hills sometimes, so maybe a bit of effort.

I do not have a proper Motorbike driving license and have only driven a scooter 3 times my life, once in Bali, so let's say i am not experienced. I wanted to rent a scooter on one day and drive along the coast, but actually it's quite a difference to Bali for instance. The streets are built as fast tracks and especially spanish bus drivers have a crazy style, so if you are not born with Motorbike skills, you should maybe take the bus instead as i did. They also rent out mainly the big fast scooters, since in spain that is allowed to be driven with a 3year old driving license. Remembering me only driving 20km/h at Bali, maximum 40, i thought this might not be the best idea.