The practical challenge on this itinerary is the eastbound overnight leg, whichever hub you choose. Flying LAS to LHR, AMS, or ATL/MSP puts you on a plane during US evening hours and lands you in Europe the next morning, so the enclosed-suite products from British Airways, Virgin Atlantic, and Delta have a real edge — a door and a flat bed make a meaningful difference when you're trying to sleep through a six-to-nine hour segment before a same-day connection to Madeira. KLM's seat is comfortable but not private, which some travelers don't mind and others do. Whichever hub you pick, build in at least 90 minutes of connection time, since Heathrow and Amsterdam can both run security lines that eat into a tight transfer.