Cartridge BBs have to match the crank as well as the bike. It appears your bike is BSA threaded so you just need to know the width of the frame - either 68 or 73, easily measured with a ruler. That width plus the width needed for the crank determine the cartridge BB to purchase.
You can either pull the BB out of your bike to see what it is and if it will work or order a new one in the recommended width with the crank you are looking at.
You should look at a modern crank like a Deore or similar.