20:1 odds it's a 1-1/8 steering column. You can confirm this with a ruler. Use a 5mm hex key to remove the top cap screw and cap (don't loosen the stem clamp) and measure across the hole at the top. You don't need great precision because it'll be either 1" or 1-1/8", and if you can't tell them apart, quit now.

Next you'll need to know how tall, which is another simple measurement, from the top of the fork crown (bottom of the headset) to the top of the stem. Consider this the minimum length when buying a used fork, new ones will be plenty long and need cutting down.

Your real challenge will be finding something decent within your budget, but be patient and you might find a cast off decent fork from someone who upgraded.