> What’s the cheapest (new) computer that can drive a 1Gb port with NAT?

What's the cheapest new computer you can find? That will work. If you have PPPoE, you need to be a bit more careful; depending on your OS and NICs, it's possible for inbound traffic to only use one core; low power laptop cpu may not have enough throughput from a single cpu, but my information is a little dated.

I did 1G NAT on a dual core haswell [1] for a long time.

[1] https://www.intel.com/content/www/us/en/products/sku/82723/i...