I don't think a single speed is a good idea, especially if your not toughened up to it. You really need to be able to keep up a steady cadence, 60 - 70 rpm and being able to shift gears is critical to that. Higher rpm's (and lower resistance) will also allow you to go further. At your stage I don't think it's a good idea to think you'll toughen up to the resistance. Your knees don't work that way.
Also, do some hydration before you start. If you wait till you're thirsty, you're behind your body's need and you won't catch up while exercising. Drink a half bottle of water before you head out the door. And have a banana. It's one of a cyclist's best friends for energy and potassium (which you sweat out).