What do POS systems cost typically? For example, what does a standard credit card reader cost, and is there additional transaction fees ontop of what credit card companies charge?
Pricing is fairly opaque in general, likely due to the sales structure and cycle. Probably the closest competitor here is Clover, which Google Search found with a cost of $999 for the first device (apparently subsequent ones are $1249). There's an additional software and service fee ($39/mo first device, $25/mo additional devices). So, comparable.
This is just for the hardware and software though, actual payment processing requires a merchant account that charges fees. Everyone has to pay these. If you're small, there's programs like these that are designed to get you your first merchant account. If you're big, this is a negotiation process where different sales departments will try to match or beat your current rates.