It depends

Because polystyrene cement does not stick well to paint (not at all really) it is best practice to ensure there is no paint where you are going to put cement. Besides, the cement will break down the paint and ruin any exposed surface.

But it’s easier to paint on the sprue.

While sometimes true that simply means you have to scrape the paint off of the surfaces that will be stuck together. Then touch up with a fine paint brush if any cement gets where you don’t want it.

What about other glues?

Super glue (aka CA short for cyanoacrylate) will stick parts together but polystyrene cement welds the parts together. CA works best if the parts are NOT both polystyrene plastic (like plastic+resin, plastic+metal, or plastic+wood). PVA (aka white glue or school glue) works best with clear bits as it won’t fog and cleans w water. Plus PVA isn’t a strong bond.

So, build it then paint it?

A little of this, a little of that. Generally the best approach is to build as much as you can easily paint once put together. The island on a carrier is easier to paint when still separated from the deck, but trying to paint all those individual parts of the island separately is a real pain given that cementing them together ruins the paint. Then glue the painted island to the painted deck with PVA and clean up excess w a wet paintbrush.

TL;DR:

Build as much as you can easily paint once put together.