I might use the first one, I don't use the second one as I think it sounds a bit silly and old-fashioned. 'For goodness sake' is still reasonably common in the UK, but with no one really caring about 'taking the Lord's name in vain' (whatever that means) any more people more commonly say 'for God's sake', '(oh) my God' or something a little stronger. They're not used in the same way. You use 'for goodness sake' or 'for God's sake' as an expression of exasperation or frustration. You would say 'my goodness' or '(oh) my God' if you were shocked or surprised by something.

As a native English speaker, I generally don't use either. They are a bit like "Oh, gosh!" or "Gee, goley/whiz!". They are much softer versions of 'God damn it!" and "Oh my God!" which can sound a little rough to some ears. I hear a lot of people, myself included, say "Gosh dang it" or "Oh my gosh" more than the two I just mentioned. They are softer and you don't have to worry about offending someone. My experience has been that usually older folks or more religious folks use these terms though I'd probably try to use them if I were around older folks or people that I know are sensitive to the use of saying the "Lord's name in vain", i.e. God.