Skyteam are definitely the best represented alliance at SNN, with DL and CO both flying to NYC from there and AF having just introduced a new SNN-CDG route (twice daily).
In *A, only US flies to SNN (PHL-SNN) and there is no OW presence in SNN (although AA codeshare on EI's tatl routes).
That said, the future of US airlines presence at SNN long-term after the Shannon stopover is completely phased out is not entirely clear. AFAIK, DL is giving up on the SNN-ATL and I am not sure whether the other routes are year-round or seasonal.

On balance, I would imagine that ST would probably make more sense. OTOH, if you do a lot on LON flying, then BD might make sense and you would get access to BD lounges with a silver card, for which the threshold is low (16K) but only when flying BD themselves and only BD-operated business lounges (not those of other *A partners).

Something else worth considering if you want lounge access but don't fly enough to make it to elite is prioritypass. It may or may not work for you depending on the airports you tend to use and priority pass lounges are often sub-par generic ones but it normally still beats hanging around in the public areas of the airport.