I had a Caddx NX8E system before rebuilding our home. It was a great
security system, and could be integrated to home automation with a
little effort (and $). It supported GE/ITI wireless sensors which are
excellent.

I now have an Elk M1G which is very easy for a DIY'er to install and
maintain. I think it will do pretty much everything you're looking
for, but will exceed your $350 project cost by a bit. You can access
the M1G via your cell phone to determine status and to control pretty
much everthing you would want to from a remote location. Internet
control is available at extra cost.

Check out http://www.elkproducts.com/products/m1/m1main.htm

I would encourage you to do hardwired sensors as much as possible. The
money you save over wireless can be put to better use in the control
panel itself.

I do not have any financial interest in any of the items I recommend.

Others here are intimately familiar with the system you''re looking at
and will likely give you some good advice.