I had trouble finding one with an am tuner which was on my feature list. When you want a couple of features the range really shrinks.
This ticks next to none of your boxes but is was cheap ($60) from the good guys. Just called a Laser, 3 1/2 inch speaker, am/fm/dab+. Only 10 presets and volume buttons but they are raised nicely out the front of the unit and easy to use.
A great unit to take out to picnics, parks, sport etc but not a party unit.