Most of the AM/FM radios I've had with external antenna and ground connections for AM have been at least shoebox size to accommodate the coils needed, and all of them are around 50 years old. A couple more than 80 years old. All with vacuum tube detectors and big tuning capacitors. None of it special, just the standard AM-FM consumer grade stuff post WW2 to the beginning of the transistor radio era.
I haven't bought much solid state equipment, most of the early portable transistor radios were not very good AM or FM, but they were portable, and quickly became cheap. I do have one solid state hifi receiver I chose for its excellent AM section (Yamaha CR-2040) as well as its clean high-power output, but that one was not inexpensive, and since it predates switching power supplies, weighs about 15 pounds.
So for low cost, I would be looking antique stores, garage sales, asking "does that work, let me try it."
Serious AM DXers go back to some serious equipment, but a lot of this is investment grade collectible now, even if it doesn't necessarily work.
Here is an
AM DX equipment recommendation from "Johnny Novice" but what he is talking about may not be the type of entertainment equipment you are thinking about. But then, there is very little today that is targeted to the low cost home entertainment market that is truly good for AM. The AM tuner is usually the cheapest thing they can put in to say that they have AM.
