I, personally, think that Venice on Archipelago map is a good choice for Diety. Sure, there might be better civs, but Venice is just so much simpler to play as, much fewer variables to manage. As such, I think it's easier to do as well as possible with Venice on Archipelago.
Actually, I just finished my first BNW Diety game, as Venice. This is my general strategy idea:
Of course, aim for diplomatic victory, you have all that gold for a reason.
Don't make any Merchants of Venice. Use the one from Optics to ally the closest city-state as soon as you're able to take the unhappiness. Since puppets produce MoV's on their own with their gold focus, you can get any more you want from there while your capital focuses on the more important GS's. I generally use a second MoV for another puppet, then plant any others to boost Venice's base gold further for trade and to avoid running out of Delegates in the WC.
Prioritize cargo ships, of course.
The way I see things, in general the main purpose of puppets as Venice is to a: serve as forward-trading bases when cargo ship distance limits are smaller, and b: to grow your capital even larger with food boats. As such, I generally recommend replacing any improvements on tiles without strategic or luxury resources with trading posts, or failing that, maybe even just delete improvements to avoid unhappiness.
Venice is made for freedom: you really appreciate those tall empire boosts, and the 3rd tier ability is amazing for diplomacy victory; you pretty much are just guaranteed every city-state alliance (as long as AI doesn't pass Embargo City-States. In my game, they managed to keep that one in play for about 50 turns until I repealed it, which seriously, seriously hurt.) On the other hand, the fact that a: AI loves order and b: the fact that you have only 1 city really producing defensive culture means that you will be hurting with unhappiness -- thus, why I recommend avoiding growth in your puppets.
You don't need to worry about AI's taking your cities all that much, as AI is terrible at naval, but with their tendency to have their fleets spread out everywhere, war will frequently result in the loss of many trade routes. Use your superior gold income to bribe them into warring amongst themselves, as well, to prevent them from attacking you in the first place. Eventually, though, I find that in late-game, between Ideology and World Congress, they will probably eventually get angry enough for someone to bite the bullet and attack you. In that scenario, I really recommend privateers, as the AI's massive but slowly-arriving navies will provide perfect fodder for building your own fleet.
Also, I can't emphasis this enough: focus on science. You only have one city to reliably make it with, so it's even more vital. Settle next to mountains if possible(as long as Venice remains costal, of course. Actually, that's why I selected 3 billion years in advanced settings, so I could be more sure of a mountain without re-rolling.) Beeline Education, Scientific Theory, and Plastics. Always run Scientist specialists when available. Don't use engineer or merchant specialists, or if you do, make sure you don't get enough points to actually pop a great one in your capital and increase the Scientist cap further. You really want to get to Globalization and finish the game at the first WL vote.
With only one reliable city, you really shouldn't expect to get a religion. You can try and pick up a pantheon, though; God-King is really nice for Venice. If by some miracle, you get one, I'd recommend picking up World Church for founder, as the flat culture goes well with Venice's lower culture requirements and weakness to tourism.
As nice as they are for Venice, Colossus is a bit off your tech route, and Petra has a tendency to disappear early, so I wouldn't really aim for them unless you have a desert blessed capital.
Also, a little tip -- you can look at the diplomatic menu to see how much gold people have for resource trades and RA's on your next turn between turns, for more efficient usage of time.
Finally, good luck! You'll need it.