OP, a big part of designing a miles/points strategy depends on travel habits. Some travelers, as part of their business or lifestyle, travel frequently... and have the right credit cards as SUPPLEMENTS to their strategy.

You mentioned that your schedule limits you to a few weeks of travel a year. Then your main (perhaps only) source of miles and points income would be via credit card bonuses. For that, as everyone else has mentioned, your biggest asset is strong credit. Try to get at least one credit card per bank (Citi, Chase, AMEX, etc.) and work from there. Discover is kind of off to the side as they don't have a strong travel/reward program.

Alternatively, you could consider making mileage runs to rack up butt-in-seat miles the old fashioned way. The miles you earn this way, supplemented by a co-branded credit card's sign-up and spending bonuses can get you where you want to go... literally.