I have both Lie Nielsen and Veritas planes and both are wonderfully made and a pleasure to use. Neither needed any work out of the box.
A 5 or 5 1/2 is a good first plane. You'll be able to flatten boards like you want and joint smaller boards as well. Flattening can be quite a bit of work where the lighter, smaller 5 will allow you to work longer without needing a break. I do like the extra weight of the 5 1/2 when using it with a shooting board though, especially end grain.
Chris Schwarz recommends a low angle jack as a first plane for beginners.
They all had made up their mind. You don't need to know the others decision to answer No to the question, but you do to say yes. If the first didn't want a beer they could definitively answer no. They did, but didn't know the others decisions so couldn't say yes. Same with the 2nd. The third could say yes because he knew the other two didn't say no, so whatever they wanted was the answer