To summarize:
POW:
Selects proposal based on what node is making it.(selects potential proposal based on node who first solved POW)
Ideal:
Selects proposal based on best proposal for the current conditions
(Selects node based on best potential proposal)
It's not any first, it has to meet the difficulty too. And this is important because it also regulates the speed of blocks being mined. "First" is relatively easy to quantify.
"Best" on the other hand... who and how to decide what's best, in an unbiased way, plus to make sure it's not cheated and also making sure the blocks are mined at the correct speed? (The who part is meant to be a trap, since the only correct "who" is the nodes.)