which budget FM Tuner

I have a Pioneer TX 800 silver face that would fit the bill. 100 bucks shipped

NAD 4300.

Denon (Japan).

What fun! vintage tuners! You should have numerous options in great gear at the used $200 price point. ...And, if you don't like it -- hello audiogon and good-bye experiment.

I picked up a SUMO tuner last year, and it's quite the little tuner! Great sensitivity.  I also bought my kid a used Cambridge Audio tuner (much more recent). It sounds great, but probably isn't "vintage".

old Yamaha (like I have) or a Blaupunkt car radio with a power supply (!)