The Wifi that comes with your rental house or at a village restaurant is likely to be basic BTL DSL. It will be slower than what you're used to at home but is fine if you're not in a hurry. And not being in a hurry is what Caye Caulker is all about! You will be able to upload photos, but it will take awhile. Graphics heavy websites may load a bit slowly. Don't expect to be able to stream video. Sorry, I don't know anything about accessing the internet from cell phones.
The farther away from the village the slower it tends to be. And maybe due to usage patterns or for whatever reason, to me it seems faster in the morning than later in the day or at night.
Have a great visit!