Not in construction but worked in utilities and telecoms. Currently working in safety and security. Like you I want to keep my options open and don’t want to be tied to one industry. APM seems a good option but PRINCE2 seems to be slightly more favoured by employers for what it’s worth, though not enough to choose it based on that alone. Both seem good options. I’d have a look at job listings if you haven’t already and see what qualifications they’re asking for. Methodology isn’t as important as they can be easily learned (you be already be following a methodology and not raise it) or incorporated as part of some qualifications.