For the asker, here is something to consider for one of those specific training possibilities! If it’s pure strength your character is after, without attention to looks, then SOME body fat is actually going to be an inevitability.
You can’t build additional strength/muscle in a calorie deficit, except under very specific circumstances (very fresh beginners chewing through excess body fat stores as “free” extra calories, steroid use - and even then!) So what a lot of the “ripped” guys do is alternate heavy training with an abundance of calories (see: “Gallon Of Milk A Day”), including the fat gains that results in, with calorie deficit periods to “cut” the fat and training designed to retain as much of their hard-won lean mass as possible (going home to a can of tuna and crying). Getting ripped, in short, is a time-consuming pain in the ass.
See also the difference between this bulk/cut fitness fella:
(Martin Berkhan of Lean Gains)
And this slab of man-beef, capable of a 900lb deadlift and a 705lb bench press:
(Strongman Nick Best, a liftbigeatbig.com athlete.)
Not to say that Martin isn’t strong, but he also values a very lean physique and puts the time in to attain it. For someone like Nick, it would detract from his training for pure strength - and despite what his BMI would probably indicate at a glance, I’d say it’s more likely than not that he IS healthy. A heavier character is not always going to be in poor health - someone who lifts as heavy as Mr Best likely has a heart like a horse.
Great further elaboration on this topic.