Update: I will be able to meet with the seller, this next Monday since I am travelling to this city. So I will check the saxes in person. Is there anything I should not miss, underestimate or forget when checking them?
OK well that changes things. So you will play test all ?
That will tell you everything.
Check if all notes 'speak' easily or not. Does any note 'vanish' or jump to a different octave ? Do you have to 'try' a note three or four times to finally get it to speak ?
This indicates leaks. Better not to put the responsibility of getting the leaks repaired ON YOU. Ask seller to attend to that.
Intonation...yes useful. Bring a tuner. If one sax seems more in tune on all notes up and down the registers, that would give it an advantage. NOTE - "in tune" means within around a ten cents variance up and down all notes. For me, for vintage, I actually say 12 cents off is even acceptable on a playtest. So do not get stressed about notes which are 5 cents flat or sharp....that is a meaningless variance.
But if you are getting 15-20+ cent variances on, say, three or more notes, on a certain horn....then that horn would fall to bottom of the list, IMHO.
Then lastly, feel and tone. Do all note fingerings feel easily accessible ? Or do you have to 'reach' your finger for certain ones....or do your fingers feel squeezed kn certain places (meaning they actually touch each other where you want some space).
Are any keys DIFFICULT to press ? Requiring MORE finger pressure than is comfortable ?
Good luck....let us know.