What is the best way to win a game?
There is no one best way to win 7 Wonders. It is a game all about adaptation - adapting to the cards you get and to what your opponent(s) play. Certainly there are different considerations for 3- or 4-player games vs more players (as with fewer players you will get to see the beginning hands in an age again).

Gunning for resources does you no good if the guilds you wind up being able to play aren't very useful - or the other cards you have to choose from need different resources than what you have. On the flip side, having a lot of resources can be a boon if you build some of the later yellow cards. Chain building is good, except when you need to build a guild or some of the blue cards not on the tech tree.

One or two military cards can be all you need, or you might need to play two per age to keep up with opponents. Or you might decide to just throw in the towel on military and focus on other aspects of your city. Military is worth at most 18 points (or a 24 point differential), but if you can at least win in the third age that drops to 8 (14) points. Building a 3-shield card in the 3rd age can be a nice way to offset some of your early losses.

All that said, you do want a few of your own resources available - that's inevitable. Depending on your wonder, the combination brown resources are great for this. Having trading posts can allow you to operate with fewer of your own resources, and the yellow resource cards (Marketplace? Don't have the game in front of me) are a lot more flexible than a single brown or grey resource (plus your opponents can't trade for those resources).

One other aspect is that green cards can be quite powerful, if you can get the right combination (a lot of one symbol or a lot of sets; having 5 cards of various symbols doesn't lead to a lot of points). Unfortunately, your opponents may see that strategy and start to build / bury the green cards before you can get them. 

In the end, though, it all comes down to what cards you're dealt and what cards your opponents are playing.