With Venice, you only have 1 city. For a normal game, people can adopt 3 trees but with Venice you can adopt 3 trees easily.
Venice is good for diplomatic and cultural victory.
For the diplomatic path: Go full tree on Tradition. These are Wonders that are ranked in termed of important for this type of victory
1- Colossus: Addition 1 trade route but 2 for Venice
1*- Petra if you have desert start
2- Hanging garden: Good because you will need a huge capital city
3- Stone henge: Give you 5 faiths and 1 GE point. It should be your very first wonder for religion but on harder to get on Immortal or harder difficulty
4- Fobidden Palace: Good for all diplomatic victory.
5- Wonder for additional spy (Forgot the name): So you will compete with other AI for CS alliance and it is quite inevitable that they will start hating you. So, how to do it peacefully. Wait for their alliance to fall out and gold gift them or send a spy to reduce their influence at that CS.
6- All piety wonders: Hagia Sophia, Borobudur, Great Mosque if you choose to go religious (which I highly recommended). By the time you get to this point, you should have 1 Great Engineer. Use him to finish Hagia Sophia, get the great prophet, make it an enhanced religion or a tile improvement, then switch to borobudur as it is in a lower priority for the AI, then the Mosque. As for religious, rush a shrine first and you should choose 15% Wonder production as your founder belief. Together with the 15% wonder production from the tradition, you can secure a stone henge and colossus and maybe hanging garden within 40-50 turns.
7- Big Bang: Reduce gold purchase. At this point of the game you will realize you wont produce many buildings but wonders and you need money for your military and building. So this is a very good wonder on you. The reason it is quite in a low priority is not many AI will adopt Commerce and you will have a decent chance to finish this later.
8- Chichen itza: Longer golden age means more money. Golden age gives you more gold and production. More time in golden age means more money, more CS ally. Hard to get actually because this is the top tier wonder list of the AI
I would suggest to spend your money on building and military units. As long as you are not in the bottom list pf military strength, you are fine.
Usually, a civ can adopt a maximum of 3 trees but with Venice, only 1 capital can help you adopt 4 trees totally (3 full trees before an Ideologies)
The tree you want to adopt is
1- Full tree in Tradition
2- Open piety but finish later or situational as you want your religion to make better relation with your CS (Check out my religion guide
http://forums.civfanatics.com/showthread.php?t=525113). Go full tree later when you get what you needs
3- Patronage is a MUST
4- Commerce: Especially good on this Civ as you will have more money and can have more gold gift to CS
5- Freedom ideology is another must because it has a lv 3 tenet that give you 4 influence per turn with CS you have trade route with. So, usually you can rush Colloseus but not Petra which will give you 14 trade route totally. You will have at least 14 alliances for sure with this policies only.
Playing with Venice on harder difficulties will result in constant war with aggressive AI. The trick here is to never let you fall bottom in the soldier point on your continent. Check the demographic data and buy/upgrade soldier so that you have a decent amount of them in your capital.
Don't use your first Merchant to buy off CS as you will get nothing or no new units. Just get a tile improvement because the extra money early game will pay off huge late game. Buy military unit, finish CS quest. Get horse to buy 1-2 horseman/chariot archer for faster camp and buy triemes to secure your trade route. 1 mistake most people make when playing with Venice is their military strength. Yes, you will shine but not necessary early game. Spend money on your military and HELP YOUR ALLIANCE DEFENSE AGAINST AGGRESSIVE AI. This is very important because if they finish them off, who do you think will be the next target? You dont want war in your capital. Make it somewhere else.
You will shine when the World Congress is found. If you have enough delegates, go for Standing Army tax because you love peace when playing this Civ. Always check for your relation with the AI as it will affect their declaration of war on you.
Focus on Building that generate Food--> Production --> Beaker --> Faith in term of priorities. You don't have to worry too much about happiness or gold as you will have A LOT with Venice.