So you apparently have fuel, and you have reconfirmed you have compression. So now you are back to ignition. Frankly, I would probably err on the side of caution and install a condenser and points only because they are inexpensive. If you can clean the plugs with a spark plug cleaner, I would go ahead and do that, check the gap. If not, put a new set of plugs in as above recommended. Just curious, what plugs are you using? The plugs need to be clean and dry in order to fire. You will have to take a look at your coil next. Early chevys used a firewall ballast resistor, 3 ohms maybe, to knock the voltage down so the points would not pit up. The coil did not have any resistance built in. The thing is that some coils are manufactured with the 3 ohms built in. You don't need the resistor with that kind of coil so if you are using one with that kind of coil you are at like 6 ohms. Might be an issue, you will have to check the coil. You should also check and clean all of the connections, including at the distributor.
If you remove the nut, wire and little metal cover on the side of the plastic distributor bushing, look in and you will see a ring slot nut. When you replace the points, you loosen this ring slot nut to remove and install new points. It can get pretty cruddy and corroded in there so take it all apart and clean it good so all nice clean contacts. After you install and adjust the new points and condenser, but before you reconnect the little coil wire, use a multimeter and confirm that the points are actually breaking the circuit when they open and close.
Head to the cap and look inside for cracks, badly pitted contacts, dirt, grease. Pull each of the wires and the center coil wire and inspect the ends of the wires and the cap tower contacts for each cylinder. If messed up, just replace. Same with the wires, they need to be clean and no cracking, don't let them lay on each other directly. Causes cross fire. These wires originally came with a little triangle wire separator to keep them apart.
