2 tips for playing Venice regardless of the victory condition:
1.) I usually buy 2 and only 2 City states. You want 2 water-based trade routes feeding the capital as early as possible and pretty much throughout the game. Both occur very early, you get one free MoV with optics and the other by filling the market which is built/bought immediately after discovering currency. So early, in fact, that Venice is often the civ that I achieve 3 cities earliest with. Also, there's usually two city states that are close enough to Venice that you don't need to guard the routes, which is otherwise frustrating early-game as fewer cities + more fogbust units = supply nightmares. It's nice when you can take one with lots of advanced units, but location is a far higher priority than units.
2.) Venice is the only civ that I spend time moving around great works. Between the puppet penalty and the fact that players usually spend most of their focus on the capital, the puppeted CS's expand their borders far too slow, and I used to catch myself having puppets running 5 or 6 unimproved tundra tiles. While you can never control which tiles they work, you can control the options for which tiles they work. Plus, while Venice doesn't have any culture bonus, they usually get to the capital's 4th and 5th rings far earlier than other civs, even the ones that have culture bonuses.
As far as victory condition bias, I don't think Venice leans too far in any direction. I find culture to be the most natural victory condition for Venice on immortal difficullty and lower, but not for deity (Deity CV games, in my experience, involve or even necessitate conquering the culture leader's capital, which is quite hard for Venice while otherwise preparing for a culture victory.) Peaceful space or diplo works pretty well with Venice across all difficulty levels; aggressive space or diplo isn't well suited to Venice.
Domination with Venice is... different. I wouldn't say easier or harder, just different. The fundamental tactic I use is Trad, partial commerce, ratty, and autocracy, then combine mercantilism/Big Ben/mobilization (2 SPs and one wonder all of which decrease unit price) combined with the incredible economy Venice can muster to be able to buy 2 or 3 units every turn. Good news is that it's one of the most devastating methods of military production in the game, bad news is that it requires a late start for aggression, often too late for deity level. But then there's water maps
Water maps are vital to Venice. IMO, Venice is THE MOST coastal oriented civ in the game - more than England, more than Polynesia, more than the Ottomans. Their trademark feature is their trade routes, and these are twice as effective with cargo ships as they are with caravans (either internal or external.) Additionally, and many players , great players, who play only pangaea maps completely miss this: the great galeass is an awesome UU. Not quite as good as Keshik/Camel Archer, but the next best one in the game (maybe impi ties it.) The normal galeass is an incredible unit for water map doms, essentially a coastal catapult with twice the moves, doesn't need to set up, and damages units as effectively as it does cities. Having that unit buffed with it's UU stats is insane. If all civs can be reached by coast tiles (which happens about half the time on arch maps), this pre-renaissance unit can be a game-ender.
