There can be bugs, however not "usually" on the beach. Most of the time there is a strong breeze blowing in off the Caribbean Sea. This keeps the bugs at bay back in the "Jungle". That being said I always take bug spray when I visit Mexico...some times I need it, most of the time I don't.
Actually the wild areas of coast are great places...granted I am outdoors kind of guy...but there are many things you can do: hike, bird watching, visiting a cenote, 4-wheel drive tours etc.
As far as "animals" there are no lions and tigers or other such man eaters. However I believe there might be the odd Jaguar. But they are reclusive animals that probably do not venture anywhere near the resort or any people for that matter.
Congratulations on your marriage and have a great trip!
Neal
neal@caribbeantrip.com