IMO, if the bike is kickstart only, a 5AH battery should be enough.
About the only big drain on the battery is the headlight and if yours is one of those RE's that uses a AC power from the alternator to light the headlight, it won't even have to do that.
By the way, if your RE has a switch to turn on the headlight, turn it off while your trying to figure out what the problem is.
For what it's worth, also IMO, your 11.7 volt reading from the existing battery should be more than enough to make the ignition coil fire a healthy spark at the spark plug. That assumes the main fuse is good and all of the wiring connections are making good contact.
About those ignition points: After you remove the cover you should see the points. They will have a spring on them and a little fiber block that is rubbing on a cam on the shaft. An electric wire will be attached to them along with a wire coming out of a little tiny "can". That can is the condenser.
You seem to have a volt meter so, with the ignition switch turned on and the kill switch in the "run" position, checking the voltage between the nut that holds the wires on the points and ground should show almost a full battery voltage reading. If it doesn't, there is a bad connection somewhere between the battery and the points. It could be a fuse, a bad wire connection or a bad ignition switch.