If you already have a USB 4G dongle you can put it into a cheap 50 $ router like TP-Link MR-3420 ver. 2. Note, only ver. 2 supports 4G. It works for me but I prefer a real 4G router.
Verizon must give you a public IP address open for incoming traffic. If you get a private IP adr like 10.9.x.x or 192.168.x.x as WAN IP adr it can't be accessed from the internet, thus you can't connect to it and manage your radio.
The speed of a 3G connection is more than enough for RemoteRig, but ping time/latency/jitter might not be adequate. In this respect 4G/LTE is much better, so get a 4G. If only 3G is available some tweaking of the advanced parameters in RemoteRig is likely to be needed as described in other places on this forum.
HNY, Palle, OZ1RH