It is with great sadness that I must announce my decision (temporarily) to abandon (land-based) Civ III and to focus on naval play. To that end, I ask two questions::
1 which is the best seafaring civ, and
2 what are the best ways of exploiting the trait?
(1) What a silly question
The English the English the English are best
I wouldn't give tuppence for all of the rest...
(2) Seriously though, I think it depends (as always) on what kind of game you want to play, on what landform and map-size, and at what difficulty level. The SEA trait is pretty useless on a Pan-map, so assuming you're going to start by stacking the deck against the AIs by choosing a Tiny-Standard 70-80%-Arch or 80%-Continents map...
The Carthaginians might be more useful for Conq/Dom on a Tiny/Small and/or 60-70% Cont-map, so that your NuMercs can make early inroads into the foreign hinterlands -- that way, your likely early GA, possibly while still Despotic, would not happen too 'soon' before the game was finished. But if you want to go conquering on a larger 80% Cont/Arch-map at say, up to Emp, then Ragnar's probably yer man -- so long as you can be sure to grab some Iron (upgrading Archers to Berserks though... even if it's allowed, it'll be expensive!). At higher levels (or larger maps), the Dutch might be a better bet for Domination (on Cont-maps), for the food-power to compete with the AI's rapid expansion, and a
very cheap UU defender (A half-price Musket from a 1st-tier Mid-Age tech? I'd buy that for a dollar!). Or you could huddle on your home Continent, and trade everywhere, until you get voted in as UNSec.
OTOH, if you want to play a long Scientific-vic game, then the Byzzies are probably your go-to guys, at least up to Emp -- imagine being able to make your capital into your super-science town...? Or at higher levels, the English, for their double-CPT-bonus in port-towns (which nearly every town will be, on skinny Arch-maps) and 25% more cities to compensate for the lower OCN (for earning gold to buy techs); also, I do enjoy watching my Navy expand exponentially as my MoWs (and Privateers) enSlave all the AI-ships.
Maybe Spain for (cheap Religious) Culture-building ... maybe? The Byzzies are also a good option for that (and Dora is much cuter than Izzie!) -- although they do need to discover more techs to get their cheap Culture-buildings.
As for the Portuguese, just ... no. Not unless you're playing a Huge 80% Arch-map, so that Carracks can actually be useful in the
very short window of game-time before they get obsoleted... The player who can win at DG/Deity with the Porties on a Tiny Arch/Cont-but-otherwise-Random map, has truly mastered the game...