I want to have a home-network for my newly built home. The square footage of the house is about 1500 (140 sq m approx.), with 3 floors, yielding a total living area of about 4500 Sq Ft.
On the ground floor, there is a home office, with two computers and printers; and a bedroom with another computer. They will be used for web browsing, downloading and printing (I'm considering a print server).
On the 1st floor, there are two bedrooms, each at the extremities of the floor. One will have a computer for HD streaming, intensive downloading and online gaming, and the other bedroom including the rest of the floor should have wireless network coverage.
The 2nd floor also has bedrooms at the same positions, one will have a laptop for basic web browsing and light downloading (for studies) and the rest of the floor should have wireless network coverage.
The 1st and 2nd floors have TVs, roughly at the middle of the floor, which if possible, would be used for video streaming.
There are surveillance cameras around the house, which too, I want to bring under the same network.
Also, I want a guest network.
How to achieve all these, always having the maximum speed the ISP allows? I'll ask the ISP to install a gateway for my home.
Suggestions are invited.

So, what will your internet / ISP download/upload speeds be? That's where you need to start at.

Depending upon the construction of your house, how you set up the network and streaming functions will vary. WiFi 802.11n is currently the best throughput, but all streams are still going to accumumlate to saturate your base internet speed. IE, if you have 2 or 3 TV's streaming Netflix, and a couple of others streaming YouTube videos, stuff is going to get congested. Also, there is WiFi (radio) attenuation to deal with. Hard-wire ethernet is preferable, and sometimes you can use (as we do in my home) ethernet over power line modems. I think we get about 50-100mbps throughput over that. Since my internet is 25mbps max, then it works well for us. My wife has a WiFi 802.11n access point in her office, and in my office is the internet modem, connected to the powerline device. I have a WiFi access point there (part of the internet router/modem), so we can get good speeds anywhere in our house (my office is in the basement).

Adding surveillance cameras adds load to the system. As long as you only connect to them via the internet when you are not at home, that should not be a problem. Configure them to not broadcast until you connect with them, or configure them to record at intervals to a network drive on the premises.

I can give some idea about the layout of my house. Consider a rectangle, with the widths facing the north and south directions, and the lengths facing the east and west.
The ground floor has the office in the south west, facing south. There is a bedroom in the east, roughly at the middle of the length. There will be three computers, two in the office (for basic browsing, light downloading and printing) and one in the bedroom (for basic browsing and printing jobs).

The 1st floor has two bedrooms, one in the extreme north and one in the extreme south. Between, there is the living room.There will be a computer in the south bedroom, (for HD streaming, online gaming and intensive downloading) and the north bedroom will have devices such as tablets, phones, etc etc. The living room has a samsung 40" smart TV, which (??) can be used for movie streaming.

The 2nd floor has the same room layout, except that the living room space is the dining here. The south bedroom will have a laptop, for basic web browsing and light downloading, the dining will have a TV and a sound system (which too I want to use for movie streaming, if possible), and the north bedroom will have devices like mobile phones, tablets and other wireless devices.

The outdoor surveillance cameras will be placed mainly in the west of the house (roughly 5-6), and one in the east.

This is the scenario.

Re:
The download speed will be more or less in the 10-15 Mbps range.
I'll ask the ISP to install a private gateway (the device which splits an area's internet connection for various domestic houses), which I think can increase speed.
I don't know much about networking, nevertheless I've considered a design of my own. Please correct me where I'll be wrong.
I think the gateway is a modem which has one input ports and multiple output ports. Lets say, I connect 3 routers to the gateway, one for each floor. In the ground floor, I run two cables from the router to connect the two computers, and one more to connect a print server. I run another cable for a WAP in the bedroom.
In the 1st floor, I run a three cables from the router, one to the south bedroom computer, one to the TV and one to the north bedroom for a WAP.
In the 2nd floor, I'll run three cables from the router, just as the 1st floor setup.
Can this be done?

You really only need one router, but you may want multiple access points (WiFi devices) that are connected to the router. The router would be connected to the modem, or contain the modem, that connects you to your ISP. This is what I do in my home. You can hardwire (cat-5 or cat-6 ethernet cables) from the WiFi access points to the router, or you can use, as I suggested, a powerline modem if you don't want to run physical cable. In our old home, the powerline connection was a better option. If you are building out the home now, then physical cables would be better.

Your modem has one WAN port that connects you to the ISP. The other ports are basically just ports for an ethernet switch that the router contains. If you need more ports than it provides, then you can easily get another ethernet switch, and plug one of its ports into one of the router ports. I do this myself. My router has only 4 ports, but I needed more, so I have an 8 port gigabit switch to add the additional capacity. They sit right next to each other on my desk with an ethernet cable connecting the two.

Yeah, the house is on the build right now. I think it'll be best to run ethernet cables from the router to the WAPs, where I want then of course.
But I'm skeptical about the power of only one router, will it be sufficient?
Can one router cover the whole three floors, with a total square footage of 4500..?

That should not be a problem. You will need more than one WiFi access point (WAP), but each should be connected to the router. A single router should handle dozens or more IP addressed LAN devices without problem. You still only have one WAN connection (to the internet), and the router is the gateway for that. More routers only create mantenance issues. We have two WAPs, but they are configured as bridge devices, not routers.

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