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I need to monitor the current on a house circuit. 120v, 20a, 60hz. The panel mount ammeter I have needs a current sense transformer connected to it. Understanding the primary/secondary winding ratio is not clicking in my head...actually, there is a hollow "thunk". What current ratio, accuracy, and burden values would be appropriate?

What you need is known as a "current transformer". This is a plain old iron core transformer but it is rated in terms of primary current and secondary current. In your case the rating would be 20 to (your meter full scale rating). In industrial applications the meter movement is usually rated 5 amps and the scale would be marked 0 to 20 amps and you would not worry about a burden resistor. However, I don't know what you are using as a panel meter so if it is a voltmeter (analog or digital) you would choose a burden resistor with ohms rated to give your meter full scale voltage with 20 amps on the CT primary. I would recommend that you get a CT rated 20:5 as I expect this would be a standard rating and would not raise any eyebrows at the supplier end. With a few more details from you re panel meter It should be possible to come up with a good design.

Correction---On the Alternative Configuration the meter should ve a voltmeter, not an ammeter

Thank you very much. You put it in a context I didn't have. Here is the site that describes the meter: https://www.ebay.com/itm/293586544417

The site shows several digital meters including CT's which measure both volts and amps and it is very much your choice which to use. Use one with a donut (window) type CT and you will have a lot more flexibility concerning full scale rating. For example if you want 20 amps full scale you can use a 100amp full scale unit and, instead of simply running the power cable through the window loop it back and pass it through the window 5 times to get full scale reading with 20 amps. I would hope and expect that the meter has some provision for calibration to get 20 amp display. Otherwise divide the displayed reading by 5. Hope this is some help.

Thank you! This is extremely helpful.