Belgique, first off, that part son #1 mentioned won't work, it works in the opposite direction (i.e. vga to component, not visa versa)... also, typically video cameras either output a single video cable or coax (that you tune into via tv).
(Component means video is transmitted over three cables, for red green blue, and is not typical for this type of config).
Eitehr way it looks like you would need some for of converter (whether as part of your pc or standalone), would could end up costing more than a monitor supplied by your vendor.
As green granite suggested, the best solution for your needs would probably be a wireless camera you buy online and view on your existing computer, which will be a) something you can install yourself and b) allow you the ability to record (possibly even with motion detection). You could buy one of these and install yourself for less than what a contractor will charge you to drive to your house.
If you do look for an infra-red one with infra-red lights (so you can record at night and the infra red lights don't give away the fact you are recording).
You may need to put a disclaimer on your wall that the area is being recorded if you plan to a) put the camera facing outside your property (vs. your looking "in your property and coincidentally capture some areas outside) and or b) you plan to use the footage with the police as evidence.
With regards to smart wiring in your house, this is a wise thing... wireless has lots of limitations, and once all your neighbours start adding wireless you get contention and it can limit performance or even jam your wireless if there is too much congestion.
I use a combination of both.
I don't check this forum often, so feel free to pm me if you have any other questions.