Given we don't use the word 'vacation' in the UK in the same way as they do in the US, 'staycation' would never be used here. I'm not even 100% sure what it means, I guess it's a term coined to describe people who have some time off but choose to spend it at home. Everyone knows what 'look out for number one' means and I suppose it's a reasonably common way to describe a situation where someone has to put his or her own interests first.

"Look out for number one" is a common expression, but "staycation" is a new portmanteau word (stay+vacation), and I think it'll fall out of fashion pretty soon.

I would say that "look out for number one" is somewhat common. I hear it more often with a Spanish twist, "look out for numero uno", for reasons I cannot explain. I recall hearing "staycation" frequently in the midst of our last economic recession, when people would talk about strategies for cutting costs.