Are there any helmets that I can use for caving that would be cheaper to buy?
no no no no no no no
there are things you bargain shop for, and there are things you don't bargain shop for. and a helmet is one of those things. you NEED a helmet with a 4 point chin strap with a good suspension system.
you may never have a rock fall on your dome, and you may never have a fall where you need your head protected on the way down. but you're going to dink and doink your noggin here and there, you're going to accidentally stand up in a 5' tall passage, and you want a good helmet strapped on tight.
THAT SAID, you can get good deals on helmets here and there. most cavers (including myself) seem to use the Petzl Ecrin Roc, which is between $75 and $90, but starting out i got a used Camp High Star on eBay for $25 shipped and that was a good quality helmet.
just make sure you're making a purchase with your melon in mind, not your wallet.