Question
There are many different components to weightlifting. What is the most important item for weight training?
Answer
The shoes (according to page 68 of Starting Strength, and this posting).
Running shoes are not ideal for weightlifting (according to page 68 of Starting Strength).
You may want to buy weightlifting shoes from Amazon (as many shoe stores do not carry them to allow you to try them on first).
Squats and deadlifts are extremely benefited by weightlifting shoes compared to running shoes. We highly recommend you try weightlifting shoes for deadlifts and squats.