Creating a new pool

I want to better understand how creating a new pool works on UniSwap, and this is how I see it as.

Say I have 1 million tokens minted. I plan to provide half to the new liquidity pool, as well as say $1000 in ETH to create the pair. Based off of the amount of tokens provided and Ethereum provided, I have set the price.

Now for the remaining tokens that aren’t provided to liquidity, what happens to those as far as trading? Will they need added to the liquidity pool in order to be traded on UniSwap? Or are the tokens that have initially been provided to the pool are what’s used for trading, and the remaining tokens will have a value based on that initial pool?

Sorry if I made it sound a little confusing, I’m just looking for insight on how it’s properly done.

Creating a new pool