It will automatically assign a seat (if available) when you check in. You are best off waiting as long as possible.

This worked out great for me a few weeks ago. Ended up getting a 738 exit row seat (was a middle, but luckily the window ended up being empty).

The caveat being, like you said, if the flight is looking oversold. Then, a last check-in BE fare is probably first to go, at least without status. I believe elites are above non-elites though, regardless of fare.