Lots of questions. Rather than consider each item one by one, I'm just going to make some general observations. And I'm going to recommend you look over material is available on the Cisco website. Even if you choose equipment from other manufacturers, the Cisco website has some tools and tutorials that I personally think are very valuable for everyone.
Now about routers, modems and hubs. Yes, as BC programmer as mentioned a plane simple modem just as one ethernet port.
The feature that is known as DHCP is often done by the modem. Routers that do not have modems almost always have one port that is labeled WAN and that is where you connect your modem with a standard ethernet category five cable. You'll need to read over carefully the information in your wireless router documentation.
Now as to hooking routers together, one reason for doing this is to increase the range of the ethernet cable. The cable works well out to about 300 feet and then you have a dangerous picking up noise due to signal loss, cross talk or interference and other such things that happen when you have long cables. If you are satisfied with just only 100 megabit ethernet you should have no problem.
As for the wireless range, it is difficult to predict the effective range of your wireless. It is possible to get to wireless routers to work together in some fashion but it's just a lot of hassle to get the way it's supposed to. It's usually easier to set up one wireless at one end of your facility and other wireless at the other end of your facility and have them tied together with cable rather than trying to make one a repeater for the other wireless. Of course, that is a personal opinion. I just get tired of trying to go through the documentation and figure out what works and what don't work and why.
Bear in mind that when you have one router after router there is the question of the DHCP and the use of the WA N Port. As far as I know you can get routers made by different manufacturers to work together. It works for me. But it doesn't always make a lot of sense
some manufacturers use a different subnet assignment. I don't even know how to explain this in simple terms but I'll give it a try. Let's say that a router made by one manufacturer expects its local IP address to be192.168.0.1 manufacturer expects its local IP address to be192.168.1.1 and you would think because they are two separate addresses they would work fine together. That's wrong! They are not inside the same subnet. To be inside the same subnet all the digits of the opt let's must be the same except for the last. The last octet is the assignments for the subnet. Maybe that's not technically correct, but that's the practical working application. You also need to know exactly what addresses are used by the DHCP device for assignment within that range. Typically it might be all the addresses in the range of 100 to 150 in the last octet.
Now if you're an IT expert and what I said sounds like a bunch of rubbish, you're right, it does sound like a bunch of rubbish. But this is sort of information you'll get if you search around on all the forums you can find this is the kind of answers you will get when you try to run to routers together on the same network.
Oh, I forgot to mention, you need to know the local IP used by the modem. Quite often it is192.168.1.254 but there is no guarantee that it will use that assignment.
If you go to the Cisco site you'll see they offer some free and trial programs to help you sort things out with your local area network using wireless routers. These programs rely heavily upon the MAC of each device in the system. That way it does not depend upon the local IP address assignments. Is worthwhile using the freebie program called network Magic available from Cisco Systems. Go to their website and get a free download. The also have a similar program just for use on wireless systems.
Pardon me for not organizing this in a clear manner. I am a lousy writer. Hope this is how some help you.
And pardon me for misspelling Ethernet.
Oh, you don't need the N feature for a home system. Your choice.
Um mm... more misspend words. Octet means a number in the range of 0 to 255 but the frist Octlet is never 0. I think.
