Pricey. Um. Yeah...
You don't need a dedicated computer unless the location with the
camera's doesn't have a computer. In that case, almost any cheap
computer will work, even a used older one perhaps. Essentially, you
want a web cam. pretty easy to set up. For types specifically
designed for lower cost security, one firm that does this sort of
system is X-10 (www.x-10.com), though I hesitate to suggest them due
to the ridiculous snake oil flavor of the web site's marketing, and a
past history of spamming and pop up ads that makes me reluctant to
buy from them just out of spite. The make it look like this great
once in a lifetime sale offer is always ending just today... (don't
believe it.) But from a few online comparisons I did once, the
quality overall seems fairly adequate, though hardly as amazing as
they make it sound. Still, the do offer pretty much turn key systems,
cameras and software that is, supply your own computer) to do pretty
much what you're describing. I'd expect you could set up a system
with several cameras for well under a thousand... Start there perhaps
for orientation, then search for home automation systems on the web.
With some creative googling, you should be able to find what you
need. I'd be willing to bet that there's likely some way to do the
software end of this pretty cheaply, perhaps even shareware or
freeware, somewhere out there. Some cameras might already be bundled
with some or most of the software you need to connect to the
computer, and much of the rest is pretty much standard web
networking, already part of many operating systems.
I'm reminded, by your price, of a young friend of mine, just starting
out as a jewelry designer, who just finished putting up a new web
site to show her designs. Nicely done site, it does what's promised
as a simple e-commerce site. But she paid about the same price you
were quoted for your cameras to have this designed. I know a few
people who'd have done it just as well, maybe better, for one less
zero in the price... If she'd only asked me, I could easily have
connected them to their mutual benefit. ... Oh well.