From the airport to the Marriott, I'd also suggest the light rail if cost is an issue.

Very easy - follow the signs at the airport to the train station, and I'd exit the train at the "Nicollet Mall" station. Walk 1/2 block in the direction the train was traveling to Nicollet Mall, turn left, walk 2 blocks to 7th street, turn right and the Marriott will be on your right.

For the journeys outside the city I'd also suggest a rental car, you can probably arrange to pick up the car at a city center location and return it at the airport (very easy). Note - once you enter the airport off the interstate you will have passed the last gas station, fill up when you're getting close.