I really don’t get why people are so upset about the warp catchphrase thing. I think its great that there’s a tradition through Trek lore. It reinforces to me that these are all people. People working hard to advance themselves to the point they daydream of sitting in the Captain’s chair. Every single Trek nerd can empathize with that daydream.
I think it was an Archer-Class, same ship Number One was one in the first episode.