communicate with ethernet equipped device over the web

I'm hoping this question may be very basic in nature for some of you savvy networking people.

So I have device which is an ethernet equipped piece of hardware that can communicate some process values that it measures in realtime. It's documentation notes that the ethernet is

10/100 802.3-2005
Auto MDIX support
Auto Negotiation

Documentation states it can be communicated with by hard wire connection over LAN or connected directly to a computer with an ethernet cable with a web browser and setting the following programmable settings in the device:

DHCP (enable or disable, so IP from the LAN or fixed)
device IP address
Network Netmask
Network Gateway
DNS Server

I would like to be able to communicate with this device through the web by connecting it to something that has a cellular modem embedded or attached and I'm looking to determine the hardware that I would need between the device and the modem. So ideally, I use a web browser to contact my cell modem ip and gain access to this device through the web.

If you need any further information to assist please feel free to pm me. I greatly appreciate your help and would be happy to send a nice thank you gift to the person that can help me to get this accomplished.

Not knowing enough about cellular modems, I can say that if it works like any other modem, then your device might just get its IP from the cell network through DHCP.

The bigger concern is security; you may want to put a router between the two that also does firewalling and DHCP itself with NAT, and then forward only the port that the device needs to the NAT IP through the firewall. This would ostensibly be 80 and/or 443 for http, but perhaps could be mapped to something else. You could also possibly set up a VPN end point in said router as opposed to forwarding a port.

Thanks for the reply. I currently have a device that does this. It uses a static ip, but I can't figure out what it really is.

The equipment is set for a static IP, netmask, gateway, and dns server, then I use ethernet cable and connect it to this device with the embedded modem and I'm able to access it via the web with a web IP address.

Is device a router? or gateway? I know that the seller is able to log into the board itself to determine if it sees a connection to my device in the field. He's able to see cell signal strength and network connectivity.

here's a pic
https://imgur.com/a/9qbw6J6