When a group or a person cares about one thing over all others, that's the top priority. “After the flood, finding a place to live became their first priority.” Priority comes from the word prior, which means to come before something else.

Is it correct to say first priority?

Both are correct. Personally I may say 'that is our number one priority right now' before either option, however. 'Main priority' is also said, although to be truthful attaching any adjective to 'priority' could be considered superfluous.

How do you use first priority in a sentence?

He said his first priority would be fighting crime and corruption. My first priority was to play for Canada in the Olympics. The relationship between our two countries is of the first priority. Our first priority is to make medicine available to our patients.