For 50's type sound like you mentioned I'd lean toward a few possibilities
(as you mentioned the gear being used matters);

Using a mic that gives the desired sound in the first place (something like an SM-57 for the old school sound)
Using a tube preamp if possible for the old school signal
Using EQ to cut the lows and bump the upper midrange (to get that pretty much 'AM' sound)

From memory sax in the 50's was pretty defined in a mix, sonically.
To me the key would be finding that correct frequency range in the EQ for the sax track before worrying about reverb or other FX. Using the right mic helps .. if you can experiment with these first, that might be a good starting point.

A sax sounds much different when recorded with an LCD vs an SM-57 .. or even an SM-58 can sound different from the 57 .. especially when different preamps are introduced.
Just my thoughts.


Make your sound your own!
.. I do not work here, but the benefits are still awesome