work permit fee is 500, I suppose the company had paid it for you
I assume you have arrived with a landing visa(visa exempt)
6300NT is the price for getting a visitor visa for USA passport holders, these prices for visa can be found at MOFA website.
3200NT includes fee for changing visitor visa into resident visa, and fee for ARC, both can be done at local immigration office.
Work permit - visitor visa - resident visa - ARC
It is standard procedures of getting required documents to work in Taiwan, I think the problem is, whoever recruits you here did not mention any of this…