Buy new, you'll get lots of years out of them. Not going to keep it that long, tubes are a cheaper alternative. If badly dry rotted and side cracked, new would be the best. If installing tubes, I always remove the tire, make sure its clean and smooth inside and grind off any weld splatter...
Leave the starter cable off the solenoid. With a test light, or meter, check for 12v at the ungrounded small solenoid wire. With key NOT in the start position, there should be no voltage at that wire. If there is, the solenoid will be energized and the starter would always be powered. That...