If it's a satellite connection, you're probably having that little gadget you mentioned as your main web access point; I'd bet that's just a powerline adapter, while the transmitter/receiver is somewhere outside.
Still, from that adapter you can connect pretty much "whatever floats your boat", provided the adapter can hold up the traffic.
A router would be the best choice for connecting multiple devices at the same time without too much effort (and wirelessly too if the router supports it), but for an open NAT status you need a static IP, open ports for the service you're trying to use and UPnP enabled.
If, however, your ISP placed a secondary NAT somewhere in the middle (mine does that, for example), you may have to ask them to...