Don't offer them a lump sum of 6000. Instead, give them a 6-turn tribute of 1000- that worked for me, and you can use the rest of the cash on turn 1 for other things.

As for early expansion, I've found that taking Italy before Greece is easier, but really either will work.

Taking Italy will get you 5 more high-money making cities (Bologna, Florence, Milan, Genoa, Naples), two of which (Milan, Naples) are ready from the start, as well as a good castle, Palermo, and two castles that you can change one or both of into a city if you decide to take Corsica and Sardinia. It's entirely possible to play the whole game without taking Rome, as in most cases it'll only get the Papacy pissed at you.

If you decide to assault Greece first, start with Corinth- It's a good castle and makes a good base of operations. You get 3 more cities, one of which is useless until later (Durazzo), another that's decent, but not as good as Italian cities (Thessalonica), and a third that is only matched by Venice itself in money-making ability (Constantinople). You can also get a good castle to defend from Hungary at Sofia, and you can take Nicaea to finish of the Byzantines, although it may get the Turks to war with you.

You should prbably take Zagreb early whichever path you choose, but it may get you into conflict with Hungary.

Usually non-agression missions from the pope are for 7 turns, and he can call them against you for multiple factions at the same time. You can get an alliance with the pope early on and gift him money every few turns to keep him happy.

Phew. Hope all that writing helps ya.