With all that flying you do, surely you already have status on at least one of those programs (e.g. UA 1K or Premier Executive; or LH Senator or HON Circle)?
Much more often than not, it is desirable to credit all of your flights to one program.
Which airline(s) do you fly the most often? Considering you fly lots of Swiss I was tempted to recommend you credit to Lufthansa's Miles & More program. Whilst the redemptions are more expensive in points than UA's, if you are travelling a lot of Business or First class anyway then it almost evens out. On top of that, LH generally has better availability than UA in premium cabins (including very few SQ premium awards vs. UA that gets nothing, and LH Senators and HON Circle members are the only ones allowed to book First seats on the LH A380s). In addition, you can earn more miles (marginally) on intra-Europe flights on LH compared to UA.
UA, as said, has cheaper flight awards, but can be affected by Starnet blocking which restricts seeing some premium seats. The flight award routing rules are slightly more generous on UA. In addition to these redemption benefits, UA elites get "unlimited upgrades" (cash tickets only, AFAICT) on shorter flights within the Americas and 1Ks can get Systemwide Upgrade vouchers for use outside of America. Note that UA elites (Premier Exec and 1K) cannot access lounges on wholly North American itineraries, even though they are Star Alliance Gold.
Your Amex points (in Membership Rewards) cannot transfer to either LH or UA directly. The only Star Alliance programs your points can go into are SQ KrisFlyer or TG Royal Orchid Plus. My pick of those two would be SQ KrisFlyer. Whilst SQ KrisFlyer doesn't have great elite benefits (with their KrisFlyer Gold not offering more than the normal Star Alliance Gold benefits across all airlines of the alliance), their redemptions are quite reasonable (at times a little better than LH, but LH offsets this if you earn many points via flying premium cabins).
You should note that KrisFlyer points expire in 3 years. Once a batch of points is 3 years old, it will expire unless you use them before then. UA points never expire as long as your account ticks over activity once every 18 months or so. LH points never expire as long as you are a status card holder (e.g. Frequent Traveler, Senator or HON Circle Member).
Another option yet again is BD (bmi British Midland International) Diamond Club. Whilst they may not be around for much longer than 12 months due to their inevitable integration into LH Miles & More, Diamond Club has some of the most generous earn and burn rates in the alliance. They have great Cash+Miles redemption options. Before US started fire selling huge truckloads of miles, DC in some sense was the "consolidator" of premium redemptions in Star Alliance.
Hope that gives you a start!