Mac,
You're doing fine (it can be very confusing!). Your understanding is
100% correct.
When I first tried to set up a home network I had a Cable modem for my internet connection, the modem connected to a router (because the modem can only communicate to 1 device in your network), and I had two devices connected to the router so both could use the same internet connection. I wanted to make a
wired computer's connection into a
wireless connection so I bought a wireless adapter for the computer (my line of thought started at the computer instead of the internet at that point). I could understand why I couldn't connect to the router...
I find it easier to mind map all this by starting with the Internet and working my through to the last device. That way it's a
straight path till it splits (at the router).
The point is that furthest the internet could get was to my router. It didn't have a built in wireless antena to broadcast the signal so my wireless I added on the computer didn't have anything to receive (just like a radio broadcast and your car radio..if you bought a radio but there weren't any radio signals/channels then it would be useless).
Since you have two internet connections you could put the Gateway computer on one and the laptop on the other...but they couldn't share files. If you want both computer to share 1 ISP connection (either one or both ISPs) then you need a router. If you get a wired only router then you have to connect the laptop to it with an ethernet cable. If you want to use the wireless connection of your laptop then "something" has to be sending out a wireless signal. That is called an Access Point (AP), (similar to a radio tower). You can buy one separately but it cost the same as buying a Wireless enabled Router. It doesn't everything the wired one does but also sends out a wireless broadcast that you can use to connect the wireless laptop.
***I wasn't sure of a way one could take two separate routers (each connected to a separate ISP) and effectively have them communicate. I decided to ask an expert for some advice. Scott Mueller, thankfully, provided assistance in his forum. The post can be viewed here.***Since you have 2 ISPs then there isn't a
simple way to connect them to your
1 home network (a.k.a. LAN). You would have to get a
Dual WAN Router (WAN=Internet connection).
***I'd like to thank Mr. Mueller for providing all the following links.***You're not going to find one that is wireless though...so you could buy a
wireless Access Point or
Wireless Router. An Access Point and Wireless Router cost about the same so get a Wireless Router and I'll show you how to turn off the routing function.
The
Cisco RV042 is about the cheapest good Dual WAN Router. You can read, in detail, about it
here.
Check out the links, especially in the previous paragraph, and let me know what questions you have.
-Evan