How soon after a strength training workout should I eat?
And what kinds of foods are best for the first post-workout meal?

Studies suggest that the sooner your post workout meal, the better.
It is debatable but it is believed that the "window of opportunity" is 30-60 minutes after your workout. As a rule of thumb, try and have your post-workout meal directly after your workout. If that’s too soon, that’s okay. Just try to have your meal before that 60-minute window has closed.
As for a balanced post workout meal, a whey protein shake with fruit would be a great choice for it’s convenience and the speed of which the nutrients can be absorbed by the body.
Fast digesting carbohydrates and proteins are optimal for this time. If solid foods are preferred or a quick shake isn't available, then healthy food choices are a great way to go. Immediately after the challenging workout, the body is in recovery mode. This is an optimal time to replenish your body’s glucose levels by eating healthy carbohydrates. Protein is needed for building and repairing muscle as well as red blood cells, hair, and other tissues.