I agree it looks like a 319. The broken belt is a timing belt - it looks like they run about $50 to buy. Plus you would have to know how to retime the machine after replacing it. My best advice is to research about how to replace a timing belt for singer 306/319 machines and see if that is something you are interested doing because that would ibe the first step in getting that machine to sew again. Hope that helps!
MJ