Hello @blakezero,
Currently, US citizens do not need a Schengen visa for any of the Schengen area countries, and can stay for up to 90 days.
(It does look like that from November 2023 US Citizens will need to register with ETIAS before they can travel to the Schengen zone).
Regarding the time it may take to get the passport (with the visa) back from the US embassy in Warsaw, my wife had her interview in October 2021 and at that time everyone got their visa back the next day, but as @Simplytex mentions, this may have changed and it may take longer now. So not a bad idea to plan for a possible longer time.
He is also correct that technically there is no requirement how much time you should spend in the visa issuing Schengen country, but the purpose of a Schengen visitor visa is to visit the country for which you have the visa. It is common for the immigration officer at entry of a Schengen country to ask the purpose of the visit. Of course it is important to answer truthfully, so when you answer that you will not even be spending a day in the issuing country and that your intention is to travel onwards to another country almost immediately, I do believe there is a risk that the immigration officer will flag this as possible abuse, and could argue that you should have applied for the Schengen visa of your destination country. (Perhaps I am too concerned about these things, and there may be people who have had no problems spending less than a day in the Schengen visa issuing country. So this is just my estimation and opinion.)
All the best!
Wouter