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Archipelago. One of my fav maps for sure.
One of your greatest challenges for sure, is acquiring land without breaking your economy completely. Playing as Ragnar should help you in several respects; Financial trait will give you extra commerce that can help you deal with high maintenance costs. Make sure to get Currency and Code of Laws early, to further mitigate those expenses. Also, Vikings have Trading Posts, which make your early ships 50% faster, allowing you to get your settlers out faster.
In any case, production *will* be a problem. Your only comfort should be that the AIs will have the same troubles you're facing. You've been very lucky with your capital, apparently, and Moai Statues there will at least give you one city with good production; personally, I might put the statues in another city to get two cities with decent production rather than one very good, but both are choices you can work with.
Make sure that you circumnavigate. The additional movement bonus will prove very useful in all aspects of the game, as moving units take time on a water map, and any warfare you're gonna do is gonna take time as well. If you haven't secured The Colossus yet, this is of course very important for a strong economy boost. The Great Lighthouse, also, is an excellent wonder to go for.
I got the impression that you're the leader of the science pack. Good; that'll allow you to settle a bit more than you can reasonably afford, acquiring territory that will be very important later in the game. Expanding hard and sliding your science meter down to 40-50% might be a necessary sacrifice. Any and all islands of any considerable sizes with any hills is of course essential to settle, if you want some production going anywhere except your capital!
Assuming the map doesn't allow for crossing oceans with just Sailing (i.e., the map is so tightly crammed with tiny islands that you can get anywhere and get trade routes to AIs), get Optics, and subsequently Astronomy, fast. Any pagans left should get a missionary or three soon after discovering them; if you can manage to spread your religion and build the shrine, the gold bonus will be cruical to manage a large sea-based empire, as well as gain you great relations with civs, freeing you up to keeping your religion.
Also, and this is obvious, but still easy to overlook; get your navy big as nobody's business. For both attack and defense, your ships will be the make or break of military prowess. Since you're ragnar, and I trust you to circumnavigate, make sure to give your ships combat promotions, to gain an edge against the other civs. Get your naval techs early, and use your advantage to ensure other civ's navys are kept to a minimum.
That's the gist of it. It's definitely an entirley different playing style, and one that may take a few games getting used to. Other obvious (and fantastic) leader choices are William of Orange (for East Indiaman, an absolutely massive replacement for Galleon that devastates any naval opposition of its time, and can carry four units instead of three) or Joao II (for fast settler production and the Carrack unit, which is the earliest unit in the game to be able to carry military units/settlers beyond the coast).
Anyways, happy sailing. Any more questions, fire away! I'm sure there are a lot of players with valuable advice.
Edit: On a second reading of your post, I see you've got Collossus and GL. Good for you. Don't sweat the 'mids or Artemis; they're a distraction on that kind of game. You don't need to waste valuable productions on most wonders. If you can reach Divine Right early and build Versailles in a future decent production city (assuming you can settle one), it'll go a long way in giving you a lot of leeway to go nuts with settlers.
