Modem? Router? I'm so confused...?

I'm going to steal part of the answers from both Ryan and John T, who both have good answers, but just to add my own input...

A modem is the device that allows your Internet Service Provider (ISP) you sign up with (your internet account) to send you an internet signal. It allows you to connect to ONE device with a wire. Many ISP's require you to use a Modem that is compatible with their system, so you can either rent from them (guaranteed compatible modem) or buy your own (might not be compatible, but you can check with ISP before you buy). I would recommend buying vs renting because if you have the same service long enough, renting will add up (do the math).

The other device you will need to get is a Router. The Router allows you to connect multiple devices to the internet at the same time, which is what you want to do. There are different types, directly related to the speed of how fast you information to and from the router. The fastest (and most expensive) is "N". Also, you'll want to get a router that supports wireless capability (honestly, I dont know why they even offer routers that dont have wireless capability, but nevertheless, don't get the wrong one.) and yes, wireless is more expensive than non wireless routers.

Finally, there are modem/router combos. Pro: only need 1 device, and overall cheaper than buying 2 devices. Cons: if one breaks, you'll need to replace "both".

So your setup will be something like:

the wall ->modem ->router -> computer and game console and phone and tablet

A modem and a router are two different things. There are also a couple different types of modems to go with that. With mediacom you will need to get a cable modem. With att you will need to get a dsl modem or they offer them for about 8 bucks a month or so. You can also get routers along with that from them for an extra charge or not. You will NEED the router though in your case. With just the modem you would get one ethernet cable slot that will have one IP address. You'll need to connect that cable to the internet port to the router to get more IP's and get more ethernet slots plus the capability of wifi, which is the reason most people get routers. Yes you can sometimes buy combo devices but those are usually the ones that you get from the Internet Service Provider(ISP)

You need to find your Internet Service Provider. Typically, this is your cable company or phone company. You'll want to order Internet service. They will provide you with a box with a port. You'll connect that port to your computer, and get Internet.

You will probably want to pick up a wireless router at an electronics shop. You will want something that supports "n" speed - standards are "a", "b", "g" and "n" This will allow you to use your smartphone and get Internet data through your rig, rather than paying data charges.

In the second scenario, the ISP box plugs into the wireless router, which spreads signal to your devices.

A modem is the device that allows your ISP you sign up with (your internet account) to send you an internet signal. It allows you to connect to 01 device with a wire. The Router allows you to connect multiple devices to the internet at the same time without a wire.

You're obviously an old, old lady who doesn't know about today's generation. Hypocrite telling me to grow up on one of my posts yet giving stupid and ridiculous answers to others. I know you're new to the Internet, but learn that there's actually different people living on this Earth. You may want to take a break from it.

Loser!