This is one lousy planet for humanoids.
I think we need determine how can you get continuous precipitation on an earth-like planet. Clearly you need a lot of water entering the atmosphere in its water cycle. So, hot oceans are required.
Next, you need air capable of carrying lots of moisture. Air can contain over 10 times as much water at 40 C as is does at 0 C, so again, hot atmosphere. You also need cool upper air to squeeze out the moisture in the air as well as dust particles to encourage droplet formation.
Though you have mentioned mostly oceans, some island chains instead of land masses, this is an absolute requirement, as any significant land masses would likely result in at least occasional gaps of rain.
So, steamy, jungle-like conditions, on steroids. Snow is not generally compatible with such an environment, so no cold polar regions. High mountains could get snow, but are bad because the air uplift squeezes out to much water, leaving desert conditions on the leeward side. So, snow should be very rare on your world.
How do you manage to have all the necessary conditions simultaneously? Because of the continuous rain, you have continuous down-draft that bring lower temperatures down to the surface with the rain. If you make the solar flux very large to compensate, you get much thicker cloud layers reflecting the sun and I believe kill off the temperature driven atmospheric uplift required. The continuous downdraft from the rain contraindicates the thermal uplift required to cause the rain in the first place too.
The only way I can envision making this world is to make the oceans hot due to very large heat movement coming from the core, making the oceans hot compared to the upper atmosphere at all times. So in addition to the rain, you necessarily will have high vulcanism and earthquakes. I think that constant rain is like impossible even under these conditions.
Earth style photosynthesis will be torturous at best due to the thick cloud deck reducing available light, so you need a brighter sun, but not too bright. So marginal plant growth at best. Soil erosion is going to be an awful problem too.
Food sources will be very limited, probably impossible to support a large and varied biome like Earth. Much worse than you might otherwise expect.
Thick clouds, constant rain, earthquakes and volcanoes and the food is not very good either. This place is going to have lousy tourism; so there is little hope of bringing in off-planet resources that way either.
Forgot one important thing, tsunamis - lots of them. Those are really bad for small islands in the middle of deep water. Most people remember the 2 largest tsunamis of the 21st century, the Christmas 2006 tsunami (Dec 26) in Sumatra and the northern Japan tsunami that triggered the Fukushima meltdown in 2011 (Mar 11).