I think we need a Martian version of the ISS. This would make things much easier for colonizing and transporting to or from Mars. Once in place, the Martian ISS would be an outpost from which to hold crew and or supplies for Mars; of course this would depend heavily on supplies from the Moon such as Helium 3 for rocket propulsion or water for the long trip to Mars. Carrying fuel and water are two of the heaviest things for a rocket especially when trying to escape Earth's( or any other planet's) gravity.

With a Martian ISS we'd have a terminal from which to transfer with between the ISS and Mars; in other words, we'd have the infrastructure between the two ISS's for a high speed Space Highway. A moon outpost is where the Spaceships would be built and fueled, and the highway system between the two ISS's would allow for high speed travel. This same set up could be repeated around the solar system. Why focus on building faster rockets when all we need to do is build a Space Highway system using ISS stations as terminals for transfer between planets?

Back on topic, I think Mars should be first.

What's so important about Jupiter? It's very interesting from a scientific standpoint (I think I just sprained my "understatement" muscle), but for pure practicality, I'd go for Mars, then leave Jupiter for the Planetary Sciences specialists...your next "practical applications" destination will be the asteroid belt, and after that, Titan. The belt can supply you with metal ores for construction, Titan can supply you with methane (aka propellant and industrial chemicals).

As for using Phobos and Deimos as "gravitational slingshots", why bother? It's much easier to simply use Mars for the slingshot...or, if you want to be really fancy, drop in-system and use Venus and then Earth as a double slingshot (Cassini-Huygens, I'm looking at you!).