The standard wiring used in modern light fixtures is 16 gauge stranded copper. If the same in 14 gauge will fit, so much the better. The smaller the gauge number, the larger the wire diameter.
See how snugly the old wire fits in the fixture. Take a piece of that wire to the hardware store. They should be able to measure with a wire gauge what size it is. If the old wire fits loosely, you should be able to get the next larger size.
Some of the very old wires have a cloth insulation that is thicker than the modern rubber/plastic, so use the outside diameter of the insulated wire as your guide. For the same outside diameter of the old cloth-covered wire, you should be able to go one wire size larger with modern insulated wire.
Modern “lamp cord” has both conductors molded together, but you can split them into individual conductors if needed; Just nick between them with a knife at the end and you can pull them apart.
If they will possibly fit, you should use compact fluorescent lamps. They reduce power consumption by at least 75% while giving the same amount of light. A 13W CF gives the same light as a 60W standard bulb. They’re now available in physical sizes to fit almost anywhere a standard bulb will. The CFs cost more, but have an operating life at least 5 times longer than the standard bulbs. They fit the same base sizes as standard bulbs, but you should take an old bulb to the store to make sure they match. With CFs, you’ll only be using 104W instead of 480W in the 8 bulb fixture for the same amount of light. At least 75% of the old style bulbs energy consumption is wasted as heat (they are actually better heaters than light sources).