Venice gets one of the "best" starting locations. Wait for a nearby CS to become decent, puppet it, then puppet another one. I've won with puppeting only 2 CSs and by puppeting a million. Greece/Austria isn't a challenge, even on Deity. Here's what you do:
1. Settle city ASAP.
2. Get TRs (Trade Routes) up ASAP.
3. Puppet CS when it's at 7-10 pop.
4. Prioritize TRs, when you can build 10 ships, build 10 ships not a wonder/culture building. Especially on Deity.
5. Get second puppet for more money.
THEN: Either plan to use a 2-3 puppet strategy, or "puppet them all" strategy. I like puppeting 2-3.
(2-3 strategy below)
6. Buy CS allies when they are on "sale" (aka gold is more effective quest).
7. Buy more allies, until they are all allies. Use spies to rig elections.
8. If playing against Greece expect a little competition. Buy them on sale all the time.
9. If you will be short on votes, put Diplomats into friendly capitals. But their votes for world leader only.
10. If only puppeting 2-3 CSs use the rest on increasing influence on CSs. If not, be sure you can handle the happiness hit.
The AI won't buy off your allies often haha. Once you are the host, you've pretty much won. Play Venice on Archipelago, Small, quick speed, and you can beat Deity haha