Your question is a bit too general to get much useful feedback here. If price is no object, then your itinerary sounds great; if price is a factor, then you will probably save money by using one of the airline-specific or alliance-specific round-the-world fare products.

I agree that experiencing LH first-class departing from FRA, where you can utilize the first-class terminal, or MUC, where the first-class lounge is pretty much the same; and EK's first-class suites on the B777 or especially the A380, departing from DXB, are products worth trying. As is Singapore Airlines first class. SQ doesn't fly to PPT, but you could take a combination of them and Air New Zealand, which gets good reveiws in biz, PPT-AKL-SIN then connect to SQ's SIN-LAX all business-class A340-500 before they eliminate that flight around October.

Or Korean Air flies direct to LAS, though their first is not amazing.