That's a '57 to '59 Y-block distributor. ..Is the carburetor on the engine something from '56?
The points and other tune-up parts (cap, rotor) could be the same from '57 thru approx the early/middle 70's.
Don't change the condenser unless you know it's bad. The replacement (off-shore/reproduction) condensers are often worse than the one you have.
If you're changing the points, the lobes where the wiper block rubs needs a small dab of points grease.
The round black plate the points & condenser are mounted to has a circle of ball bearings under it that allow it to rotate. If it doesn't rotate it needs to be removed, cleaned, lightly lubricated and reinstalled.
Applying suction to the line into the vacuum canister should turn the round black points plate approx 1/4 to maybe 3/8 inch. That's one of the two ways it advances the timing.
Where the connection from the Ign coil passes thru the distributor housing check that the insulation isn't failing.
There should also be a 'Ground' wire from the points plate to the distributor housing. I think I'm seeing one running behind the condenser in your photos.