We have cable internet,what is the best wireless router to cover a big house

Have you checked that the signal on your new cable modem/router is strong enough to reach your wireless devices? You may need to re-site the cable modem to get better coverage in your home. Your old one probably worked fine in the same position but that doesn't mean a new one will. There are a few things you can try to get the best of the range it has. Internal walls and furnishings all play a part in reducing the effective range of the router. Most routers will give you at least 50 metres indoors. Keep the router as high and as far away from walls as you can, this will greatly improve the range. Try to ensure the router is not screened by large near by metal objects such as steel PC cases, these will absorb wireless signals and reduce the range.

Not strictly speaking.
You can use a wire instead if you have a port (hole) for ethernet plug (slightly larger than a phone port).
In coffee shops you'll be using wireless, but they provide the router.

Usually the internet service provider (even satellite) provides a modem/router to access the internet. This being said to purchase a wireless router must mean that you are going to "broadcast" your satellite internet throughout the house so that others in the house can access the internet.

In that case, no it doesn't really matter what kind of wireless router to buy. Just make sure you connect your satellite modem/router (what they send you) into the wireless router correctly. Also, make sure you put a password on that wireless router so that your neighbors or unknown persons do not gain access to your internet/computer.

Thanks.

In order for you to accomplish that goal what you need to buy is a wireless router that can be located on the other side of your house so computers there can have internet access wired or wirelessly connected to the router. You can get a wireless router from Linksys, Netgear , Dlink or Belkin.

you need a wireless ethernet bridge(like wet54g/wet610n) which will grab signals wirelessly from u're primary router wrt54g,& then a ethernet cable from wireless bridge will be connected to one of the lan port of u'rs netgear router(otherwise u will not be able to do file & printer sharing between 2 routers)Remember,the ip address of all 3 devices shold be of same class.

I presume you need Internet access in this house using a wireless network.
The best place to locate the wireless router is in a spot centrally located where the radio signals can reach the rooms where the computers are located. The DSL or cable modem/connection would also need to be in this area so it can connect to the wireless router.
If the wireless router is in a multi-storey house and the floor slab and walls are concrete and/or brick, then the radio signals will be impeded and the signal strength to some rooms will be weak.
In such circumstances, it maybe better to install network cables from these rooms to the wireless router, or install wireless access point repeaters to increase wireless coverage.
If you are not sure how to setup and install this network, then I suggest you get help from a computer savy friend or from your computer friendly shop.

if your signal is low in there the best work around would be to lay a cat-5 cable up to the router, the wired connection would be faster and more reliable then a wireless, or buy another wireless router and put it closer to the basement than the first and wire the 2 routers togher with cat5 using the second router as a fancy switch.

How far are you running the CAT5 cables from house to house?   CAT5e only has a solid range of about 150ft, and anything near 100ft is pushing it.  You may also need to use CROSSOVER cables when plugging routers into other routers. 
Also, who has the actual internet connection?  I'm assuming House 2 does.  One big problem is a router is your Gateway address.  And, if house 2 is the only one with a valid Internet connection (via DSL or Cable, etc), then the router in house 2 is the only "true gateway".  And, all 3 houses need to be in the same physical network (i.e. 192.168.1.0 range or whatever), and all computers should have the same Gateway address...which would be the IP address of the router in House 2.
What you really need in this situation is 1 router and 2 switches.  Put the router in House 2 and put switches in House 1 and 3.  That would be the best way to handle this problem.  It would also end your connectivity problems.
Cheers!

i use a adsl router,

it allows me to go wiresless on my laptop, play my xbox and use my base computer.

the gateway and modem are part of the router so only one device is required