How much are you willing to reinvest over the years, especially if you're keeping the house for 20-30 years?
Because the issue isn't just initial vs. final costs, but also maintenance and durability over time. Whoever told you about shorter timelines is right: wood construction is faster, and yes, energy costs are lower. But there's a detail nobody emphasizes enough: in the Brescia province the climate is humid, with significant temperature swings. A wooden house needs more careful and conscious maintenance, especially of the external structure and joints, otherwise moisture problems can develop over time that you won't notice right away. Traditional masonry is lazier from that perspective: it survives ordinary maintenance mistakes.
On the mortgage, banks today are less wary than ten years ago, but it's still true that they ask for more documentation and surveys for wood. It's not that they'll deny you financing, but you'll pay slightly higher rates or get somewhat less favorable terms. And when you eventually want to resell, that's a factor: in that area masonry is still what people think of as the standard, so you won't have the same pool of buyers.
The initial costs of wood are often genuinely lower, but with specialized labor being expensive and future maintenance, the savings get thin. If your goal is to live there without worrying too much about future resales, wood can make sense. If you think you might want to sell it someday, stick with masonry.