If I blink Neeko with Temporal Breach, can I choose the same legend? I'm guessing the first chosen legend ceases to exist the second Neeko is banished, so I should be able to reselect it. Follow up question: would that legend "enter" ready? Again, as far as I've read from Riftbound creators, legends do not enter, they just simply exist, so nothing says they should enter exhausted. In summary: if I blink Neeko, can I effectively blink whichever legend I've chosen with her?

Yes — blinking Neeko gives you a brand-new legend, you can pick the same one again, and it comes back ready, so an exhausted legend ability is live again.

Your instinct on the sequencing is right, and the rules support it cleanly. "Add it to your Legend Zone" is a Create action (Rule 440.5), and any legend created during play exists only for the specified duration and "ceases to exist once that duration ends" (440.3.b) — so when Temporal Breach banishes Neeko, the legend is gone before Neeko is replayed. The replay is a play, so "When you play me" triggers again on the new Neeko object and you choose afresh from your up-to-3 deckbuilding picks (same one is legal — nothing is left on the board to collide with under 440.3.c).

The one correction: legends don't "enter," true, but they are Created, and Rule 174.2.b says created legends are created ready unless the effect says otherwise. Neeko's text says nothing about it entering exhausted, so the re-created legend is ready — which is exactly why the blink resets it rather than leaving it tapped.