What are the most productive strength training exercises?

After six weeks of being out with an injury, I am ready to start running again. If I run every day I will re-injure myself, so I am going to use this as an opportunity to start strength training by alternating days.

My goals are to (1) strengthen my core and lower body so I can run faster and (2) increase muscle and lose fat so I can run faster.

What are the best strength training exercises to accomplish these goals? I have access to a full gym but have no idea how to use any of the weights or machines.