Needs to be cleaned up and needs news heads. What kind of heads would sound good on this drum?
Your head selection might be limited to what'll fit the drum. Before the mid/late 1950s, drum shell diameters were a little bit bigger than they are now, so modern plastic heads often won't fit old drums, or if they do, it's a TIGHT fit that makes tuning a bear and can damage the drum's finish.
Thankfully, Aquarian makes the American Vintage line of heads. They're slightly oversized, specifically to fit older drums. And they sound great on my old Radio King. Make sure you don't confuse the American Vintage heads with Aquarian's Modern Vintage heads, which are the same heads but in modern sizing.
Also, what are the correct snare wires? It's currently got old Gretsch Responso snares, but they don't seem right. I kniw that bridge system on there must have some purpose.
The bridges allow the snare wires to extend past the drum's bearing edges, kinda similar to parallel strainer systems like Ludwig's "Super Sensitive" mechanism. I'd recommend using the wires Puresound makes specifically for old Radio Kings because they're not only the right length, but the right width. Old Radio Kings tend to have narrow snare beds and my experience is that wires any wider than 16-strand sets may buzz like crazy on these drums.
Puresound's model numbers for a Radio King with three-point strainer and bridges like the one in the eBay auction above are PRE1416 for 16-strand wires or PRE1412 if you want a narrower 12-strand set. You can order them through Interstate Music, among other sellers.