First check out some of the webpages on cycling on Gran Canaria.http://www.cyclegrancanaria.com/http://www.free-motion.com/en/gran-canaria/http://www.cyclo-canaria.com/en/http://happybiking.info/http://www.lacicloturista.com/en/
They all want to sell you guided tours, which are a nice way to meet others, but look at their tours, the maps, elevation profiles and you'll get an idea of what's in store for you if you go there. You'll also see that most only cover the southern half or third of the island. The last link is to a cyclotourist ride in December with a really hard mountain time trial on the final day.
There is also lots of info on climbbybike.com and other sites on the individual climbs.
What might also pull you toward the Canaries, however, is GC's proximity to Tenerife. There are fast and slow ferries to that island from GC, which will offer you lots of other climbs to ride. It's no wonder that many pros ride there in the winter.
Afa where to live is concerned, I mentioned Puerto de Mogan and Arguineguin. What exactly are you looking for? If you want to live on the coast, they are nice, kinda quaint and not too small. If you want to live in the mountains, there are plenty of places to do that, such as Mogan, St. Bartolome, St. Lucia, but you might have to go to the coast to buy some bike stuff.
I mentioned no Campy because I have a Campy-equipped bike permanently on the island and one time a tiny spring in the left brifter broke, which left me with nothing else than to rent a bike - they cost more per day than a compact car! I took the shifter back home with me (in Germany), fixed it here and reinstalled it there, plus brought a replacement in case it happens again. So bring anything that can wear out to avoid long waits for packages from the mainland.