Consider LH M&M while flying UA in the US. Fly LH international, as any fare ticket can be upgraded, (it seems to me your primary objective is upgrades of heavily discounted tickets).

After you get 35K miles in M&M, you will get a 25% bonus on all miles earned (every UA flight will earn a minimum of 1000 miles). You will get double miles for business class. After 100k on LH (LH SEN), UA will usually comp some status as well. US west coast to Europe and back in Business class will net over 20k status miles.