DanTana,
Congratulations! You have one of Zenith's best AM/FM table radios from the '60s, model K-731 (chassis 7M07).
I also have a Zenith like yours (almost exactly, except for the grille cloth), an ebay score about a year and a half ago, and like it a lot, though I don't use it much. I cannot say enough good things about it. This model is second only to Zenith's model C845 in sound quality, and may be better than the '845 in that regard because of the K-731's larger cabinet and two-way speaker system. The '731 has a 5x7 oval speaker for lows/midrange and a small electrostatic tweeter for highs, the latter being driven directly from the plate of the 35C5 audio output tube.
The only modification I'd make to this excellent radio would be to replace the selenium low-voltage rectifier with a modern silicon diode (don't forget to add a series resistor to get the same voltage from this as you did from the original selenium). Seleniums were good in their day, but have long since been superseded by silicons, so I'd replace the old rectifier as soon as possible. Selenium rectifiers can short, giving off a gas that smells every bit like rotten eggs (the smoke can be toxic as well)--another case for getting rid of that old, outdated selenium rectifier. You may and probably will also find that you have more voltage output from your power supply when you replace the selenium (the reason for the series resistor). I'd go through the tubes and replace any weak ones as well, not to mention replacing old wax or paper caps under the chassis. Any radio this old is bound to have a few doubtful or outright defective capacitors (I'd check the main 3-section electrolytic in the power supply as well), perhaps some out-of-tolerance resistors, and, as I mentioned, weak tubes.
If your set works, however, I wouldn't do anything with it beyond replacing weak tubes and/or the power supply filter. In a radio of that vintage (Zenith introduced this set in the late '50s and offered it in two cabinet styles), I'd replace the filter cap as a matter of routine, even if you have no hum in the sound.