As far as I remember the US Government left ARPANET back in the early 80s when MILNet was brought up. It was eventually replaced with NIPRNET (along with SIPRNET and what ever the top secret network is called). NIPRNet carries the unclassified government data and then has Internet gateway connections into tier 1 backbone providers.
Tier 1 providers in the US are companies like Sprint, ATT, Comcast, Verizon (formerly UUNET), etc. Tier 1 providers then interconnect with each other through IXPs (internet exchange points). Most individuals are connected via a tier 2 or tier 3 ISP. These ISPs aggregate data up to regional networks that then typically transfer them onto a tier 1 network. If your destination is serviced by the same tier 1 network you typically wouldn’t cross an IXP. But the 11th hop from me to British Telecom crosses an IXP between Comcast to BT:
10 114 ms 159 ms 161 ms as5400-pe01.111eighthave.ny.ibone.comcast.net [126.96.36.199]
11 188 ms 174 ms 122 ms t2c3-xe-0-3-0-0.uk-lon1.eu.bt.net [188.8.131.52]
I am not familiar with NIPRNE, but I am assuming that they operate like a private Tier 1 provider and then use something like IXPs to interconnect with other Tier 1 providers. Their cost (if any) would be tied into some type of peering agreement.