I came this close to (doing something)

This is an expression that people say while holding their thumb and index finger close together (like they're holding a pea between them). It means "I almost (did something)":

I swear, I came this close to just punching him right in his face!

I came this close to getting killed by a bear!

People use this expression in spoken English, but almost never in writing.

pack up and move (somewhere)

"Pack up and move" describes moving somewhere suddenly:

I have a life here. I can't just pack up and move to another country!

"Pack up" means packing your suitcases, packing your things into boxes, and so on.

(go/move) out to (a place)

When people talk about going or moving somewhere far away to the east or west (but not overseas), they sometimes say "go out to ___" or "move out to ___".

I heard that she moved out to Oklahoma.

When you want to talk about someone going overseas, "go over to ___" is usually better. When someone goes to the north or south, "go up to ___" or "go down to ___" are common.

pursue a career

When you "pursue a career", you try to work in a certain industry.

This phrase is usually followed by "in ___":

I'm pursuing a career in nursing.

When I was in my twenties, I wanted to pursue a career in law enforcement.

You can also put the name of the industry before "career":

If you want to pursue a teaching career, you should take courses in psychology and social science as well as courses in the subject you want to teach.

By the way, a "career" is a long-term set of jobs that you get which are all related to each other. For example, I've had two separate careers in my life: one in teaching and one in publishing. I've had several different jobs in each career.