Here's my 2 cents on speed / distance training (and I'm not an expert, I just like to run):
When you are first starting, the most important thing is consistency - just get out there and move on a consistent basis. Since you are starting from scratch, improvements in endurance (distance) AND speed come pretty quickly at first. But, at some point everyone will reach a "plateau" where they don't see much improvement with the same program. So, to increase endurance or speed, you have to change something. And simplistically ... to run farther, you have to run farther. To run faster, you have to run faster.
If you want to increase your endurance, you should pick one run per week, and gradually increase its length. Take the run slow and don't increase your overall weekly mileage by more than 10%. That's how people train for distance events. If you want to increase speed, take one run per week and throw in some faster intervals of running. Try 30 seconds or a minute of all-out sprinting, then walk or jog easy to recover, and do that several times. Another approach is to find a hill and run up and down. Either way, you are training your body to run faster.
In my experience, you can train to increase your distance OR you can train to increase your speed, but it's darned hard to do both at the same time. I usually go for distance first, then keep the distance the same and train for speed.
There are lot of factors influencing speed. Body weight is a huge factor, on me, even 5 pounds makes a big difference in how fast I can go. As they lose weight, most people find they will just naturally get faster. Other factors are natural ability, biomechanics, general physical conditioning, terrain, and weather conditions.
And for all beginner runners: Cross training and strength training helps to keep your muscles "balanced" and joints stabilized. Make sure to stretch effectively and often. Get properly-fitting running shoes. And have fun!
<thus ends my seminar for the day>