Not a dumb question, but what you heard about "poofing out" is dumb. You can do both at the same time, and, in fact, building the muscle will help you lose the fat buy burning more of it even when you're fast asleep. There are people who fiercely subscribe to one or the other, but I believe exercise is like balanced eating. You'll benefit most by having a nice balance of all kinds of exercise. I think cross-training in all areas is really helpful.
"The grass ain't greener, the wine ain't sweeter, either side of the hill" The Grateful Dead