I have found Venice very frustrating to play. My cap is already over busy with guilds, national wonders, and the occasional WW. To that, Venice has to build all the archeologists (can't be rush bought) and probably all the work for International Projects (puppets might help, but it is very hit or miss). Warmongering with promotion-less units is less fun too. For SV, only the cap can build SS parts. It seems to me that puppets are basically spoils of war -- the outcome from your expanding empire. But puppet cities don’t directly contribute to your chosen VC and only really become productive towards that until you annex them -- and Venice does not get that option!
Of all the VC, Venice is weak expect for Diplo -- but that’s the easiest VC anyway.
Yes this is quite true. The most frustrating thing about Venice is that you only have to have a couple Civs in your neighborhood declare war on you, sack all your trade routes and grind you down by attrition and you have no means to recover.
So you have to manage your game very carefully to prevent that from happening at all costs. The Great Galleas contrary to what the Civilopedia says SUCKS. It can barely beat a Caravel in a straight fight and against a equal tech civ will take horrible damage from city attacks.
However after a playthrough of Venice I did find a pattern which I think is worthwhile following for the most part.
Basically I think ignore the Ancient & Medieval Era Wonders because none of them are essential or really that good. However the Classical Era Wonders are much more attractive and you should get a least a couple of them.
1. Build order is probably scout>shrine>granary/monument...
If you have a desert start then desert folklore is essential
2. Open Tradition and Beeline the Hanging Gardens. As you don't build settlers you will have time to get basic buildings in place to rush this wonder. You should steal a nearby worker to avoid the time wasted in having to build workers.
3) If you have desert then you certainly need to beeline Petra. It is achievable on Diety.
Otherwise from here I would probably beeline Philosophy. For me I would prioritise Oracle over the National College because I hate being beaten to Wonders.
More than anything I think Venice really needs some additional sources of culture. Hanging Gardens, Oracle, National College, National Epic & Heroic Epic will total 7 additional culture per turn and these wonders should be a fairly high priority. Also working the Writers Guild ASAP is highly desirable to get additional culture and tourism. Note that the border of Puppet States grow really slowly so it very good to have some Great Works ready so you can move them into these cities to speed up their border growth when they get Amphitheatres otherwise you will lose tiles to nearby civs
4) Once you have Philosophy I would get Optics for your merchant of Venice. Some people may wish to get Optics earlier but I think the early Hanging Gardens will provide enough food to grow your capital up until now. Citystates usually develop faster when they are not puppeted (especially in Diety, they will probably have pikemen before you have composite bowmen) so if you wait a bit longer to puppet a city you may find they are much more developed and come with a nice army.
5) After you get the Oracle, National College, Writers Guild fit in all the other essential infrastructure as required.
Try and get a religion and a Grand Temple in ASAP. A Grand Temple will really boost your faith per turn and makes your trade routes export your religion really quickly. This will also give you some faith generation so you can buy some Great Engineers in the Industrial Period. For beliefs I think 'World Church or Tithe', Religious Community and Defender of the Faith (if you have unfriendly neighbors nearby) are worthy choices
6) Your probably now in the medieval era; personally none of the medieval wonders really appeal to me as Venice so I would use this time to build a barracks and a Heroic Epic and focus on getting a decent sized army and making sure that all your trade route slots are filled. Largely because the Renaissance era wonders are much better and if you have a nice military now you won't need to worry so much about defense when you are building the Leaning Tower, Sistine Chapel or Forbidden Palace. It shouldn't need to be said that Education is the technology you beeline to.
7) From there I would strongly prioritse on getting to Navigation and building/buying a fleet of Frigates. Naval control should be one of your key goals as you want to make sure your cargo ships are protected. After this I think it is fairly straight forward, just beeline techs that have Wonders you need and make sure that Scientific Theory is high on the list.
Once you have a fleet of Frigates you can start looking further abroad and maybe a nearby neighbor has the Colossus ripe for the taking.
Social Policies.
Venice gets benefit of many social policy trees but its best to pick policies that benefit puppet cities & your economy
1) So full Tradition for starters.
2) I would then open Commerce to Mercentalism. As you will be purchasing items the 25% discount is very useful and you can buy Landsknechts to use as cheap cannon fodder if you need. Commerce is actually a very useful tree if you are intending on playing a diplomatic victory and I would take Entrepreneurship over Patronage since the Merchant of Venice is very good at diplomatic missions.
Big Ben is also an essential Wonder & with Mercentalism with give you a 40% discount on buying items.
3) From here I would probably unlock Rationalism and take Secularism and then work to Free Thought. Puppeted Citystates seem to prioritise specialists and trading posts over mines and farms so these policies will ensure that your puppets are achieving high efficiency.
4)Exploration is also an option as the opener provides a nice bonus to naval units and Maritime Infrastructure also is a real help to puppets but I tend to think that Rationalism is more important. But this really depends on how confident you are going in Science. Otherwise if you are going for a culture victory I would also be concentrating on Aesthetics.
5) For ideologies Freedom is definitely the best as it offers the most to boosting specialists, great people generation and landmarks/great person tiles. Statue of Liberty is essential.