Posture in running not only relates to your spine, but also your hips and arms. When you run slouched you keep your lungs from fully expanding and you tend to look down instead of straight ahead.
Your hip position is also critical because it determines which muscles and tendons will absorb the most impact. When your hips are underneath you, your biggest muscle groups and tendons will absorb the most impact which will help you run further and faster. Avoid slightly bending your hips backwards like you're about to sit down. This puts extra stress on all the wrong areas and you get tired faster.
Your arms need to be at a 90 degree angle, stay compact, and swing on the side of your body, not across the front of you. Imagine a line drawn down the middle of your body, and then make sure your arms don't swing over that line.
Believe it or not, your running stride starts with your arms. It's similar to two gears working together, like the photo on the right. The smaller gear (arms) moves the bigger gear (legs), so the better your arm swing, the better your leg stride. On your next run experiment by keeping your shoulders relaxed, but also driving your elbows back and pumping your arms fast. Your leg speed will want to follow.