This should be guided by the specific PFT metrics that his branch tests (Physical Fitness Test). I would work towards the tests, but also develop a general level of conditioning and competence with BW exercises. I recommend doing the following:
Look up the actual PFT for his branch. Have him perform the actual test once per week, always trying to better his times or scores.
He probably will never touch a barbell in Basic Training. There is plenty of time after Basic to bulk up and get strong. Boot Camp prep should be focused on acing the exercises they’ll actually make him do and getting through injury-free. That said, I’d keep some barbell exercises as outline below.
Focus on timed road running (and possibly rucking depending on branch). Most of the running revolves around distances greater than a couple miles. I’d run 3-5 miles several times per week.
Focus on mastering BW exercises. Some recommend doing pushups, dips and pullups daily. But I’d personally do something like this:
DAY 1: Pushups SS Ring Rows 5xMax ea.
DAY 2: Deadlift SS Incline Situps 5x10each
DAY 3: Dips SS Pullups 5xMax ea. (use banded pullups if necessary)
DAY 4: Back Squats SS Leg Raises 5x10 ea.
DAY 5: Perform the entire PFT and record score.
And run almost every day. Skinny people who can run make it through Boot Camp all the time. Get jacked afterwards…