Moving out of state

Depends on your income, what state and how much rent is. Moving to New York City for example you'd need more than moving to Indiana.

A good paying job

It mostly depends on the states you're moving to and from, how far you need to travel, and what your current income/savings is. For example I live in CA, which is probably more expensive than most states. I'd say a safe and cheap bet for most people would probably range from $2000-$5000. It doesn't have to cost thousands and thousands of dollars to move to someplace new if you're careful about it. It's possible to do this for less than 2 grand too, but personally I'd rather save up a little more than that in general since it's nice to have some breathing room.

first last & security for your new lease

plus another thousand or two for incidental bullshit

Not sure I understand the question?

I took this as how much savings would be enough to make you move to another state. Not how much does it cost or how much I would need to actually move.

All things considered, if I lived in a high cost area and I could move to another area that was lower cost and keep the same job or income, same living standard, pretty much everything the same, just new area, if I could save $1000 to $1500 US dollars a month, I'd highly consider it.