Some factors to consider:
How many flights do you expect to fly in a year, and will you be flying Business class? If it's once a year in lowest economy, then frequent flyer program doesn't really matter, just pick the lowest fare with a decent schedule. Out of the two, UA is probably better due to the no expiry policy. If it's multiple times a year in Premium Economy or Business, then you can take a look at the two programs and see which airline you'd fly most often and which one make sense.

Which city in the US are you based out of? If you are based in LAX, there are lots of options NH/BR/UA/AC/SQ/UA that can get you to SIN, whereas if you are in BOS, there's LH/TK/LX that would work. If you plan to fly a lot domestically, and you are based in ATL then committing to Star Alliance would mean you will be connecting frequently unless you fly to UA hubs.

Do you plan to spend a lot in the US using credit card? You can look at getting card that earns Miles directly (Chase Mileage plus explorer card), or a card that earns transferable points that can be converted to various airline programs that can help you earn enough points to book reward flights (Chase Sapphire that earns UR points, Amex cards that earn MR points, UR can be converted to MP, and SQ is a transfer partner for both of them). The airline cards will generally give more airline specific benefits such as free checked bags, lounge passes, discount on inflight food/drinks. High spending on US airline cards (10k+ per year) can also help boost elite status. High fee non-airline specific cards can also include lounge accesses (priority pass, or Amex Centurion, it depends on your flying pattern whether you will be able to advantages of the lounges as they are not everywhere). There are many of these cards, with different bonus categories, benefits and fees so you'll need to optimize based on your own spending habits.