The most important thing when starting a new game, be it 2 player or more, is continent bonus. With a few exceptions, the person with the most reinforcements over the long-haul has the best chance of winning.

Reinforcements formula:
A) 3 armies +
B) 1 army for each 3 territories controlled beyond 9. (i.e. 12 territories = +1 army. 15 = +2) +
C) Continent/zone bonus +
D) Bonus armies for trade-in cards

When you initially start out, B will likely be hard to achieve and will offer only a slim advantage if you accomplish it. D can only happen after at least 3 turns. But in many cases, it is possible to accomplish C within the first turn or two.

To that end, if your initial distribution warrants it, look at grabbing South America or Australia in Domination, Yellow or Blue in Euro. Using your bonus reinforcements you can start deciding where to go from there. Invade adjacent continents, or whittle down your opponent?

It's rarely QUITE so simple, but this strategy has worked many times for me before.