I usually use...
"good energy sent" for non mortality issues,
and
"all sympathy and empathy" for the more serious issues.
Not hard and fast rules, variations are possible, and sometimes I pop out with something new.
I have used "thoughts and prayers" myself, though, if I either just woke up or I'm very tired. I don't see anything wrong with it, regardless of the religious stance of the party sending the message.
Let's face it, even "goodbye" is derived from "G-d be with ye." Or so I'm told, and nobody gets ruffled over that.
Terry