Hm. Thus far, I have not played a BERT or BE game with a mind to win. I play it like Civ - I putter around a lot and then I decide on winning when I get tired of playing SimCiv. This generally takes about 200-250 turns, most of which is spent doing nothing in particular. Cute stuff.
I move cities a lot. It's one of those things. For tile-claiming, I build all the production facilities and then Tidal Turbine and Thermohaline Rudder, both of which have their own outputs. With routes coming in, this will generally move the city move to 1 turn - that's when I start moving the city.
For area claiming, I do the same thing but I move it a lot more, usually accompanied by a bunch of workers, improving tiles as I go. Usually, you only need a single city for this, and a "path" of cities you're going to leave in your wake. You move the primary city across the map, 1 tile per turn and found stationary cities in the previously claimed tiles, not necessarily aquatic cities themselves. As long as you're claiming 3 tiles per move and you work the resource tiles left behind with new cities, it's actually not too bad. Cue argument about how most of the output is in Trade Routes anyway.