WiFi should work in most rooms of the average house. You do have to have a
WiFi network setup in your house. http://wifi.aximsite.com/wifi_net.html or
http://www.wi-fi.org/OpenSection/why_Wi-Fi.asp

I suggest you do the research.
Search Google for "network cameras" and "WiFi network cameras" without
quotes.

Read the Manufacturers specs.

Wi-Fi and dialup are not mutually exclusive, as long as they are used
for different things.  You can connect your computer to the Internet via
dialup and connect your computer to a home LAN (wired or wireless)
simultaneously; what you can't do with most wireless routers or access
points is connect them directly to the dialup connection so that other
devices can access the Internet without going through your computer.

For the kind of in-home surveillance you describe, the easiest and least
conspicuous setup is a webcam using Wi-Fi networking to send its image
to your laptop.  Next best IMHO would be to use a USB webcam and a long
cable, provided the camera is just around the corner from the computer's
location.

Unless you have a wired network already installed, either you will have
to run wiring through walls (and either through the attic or beneath the
floor) -- which can be messy as well as laborious -- or you will need to
run exposed cable along walls and through doorways.  Going around walls
is unsightly, presents a tripping hazard, and requires much more cable
than taking a more direct concealed path.  Depending on how long a cable
run you need, you may end up spending nearly as much installing a wired
network as you would on a wireless one; if you hire someone do to the
installation you will almost certainly spend more on a wired network.

You might also consider one of those "X-10" system cameras that are
advertised in spam and pop-up ads.  But I wouldn't use one for the
simple reason that they *are* advertised through spam and pop-up
advertising.