There are no snakes on the island, the only spiders are little non-b iting ones, there are no sharks and no jelly fish. You'll have a safe, happy holiday!
For places to visit, I'd recommend hiring a car and touring the major places of tourist interest yourselves, you can read all about them on this site and decide which ones you fancy. Here in Costa Teguise, there's the Aquapark, which is a big water park with slides etc.
Have a great trip!
http://www.grupoestupendo.com