which budget FM Tuner

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 (!)

I had a Sumo Charlie for a short time a couple years ago, nice tuner.  I have a Creek CAS-3140 w/Din to RCA cable that is wonderful.  I've owned it for a good 6 years or more.  I've also owned some other nice tuners in the sub $200 range.  I prefer analog over digital tuners, let me see if I can find my old tuner post which lists the ones I've had, there are many good choices in this price range.  If you can get a Sansui TU-717, jump on it, but I don't think they are selling in the sub $200 range, are they???  Been out of the used Tuna market for a while as I am very happy with my Creek.