Domes are now in general use rather than traditional.
They make for a neater appearance.
Channels as you mention are one per camera, so a 12 cam system would require a 16 channel DVR, meaning 4 spare channels.
A channel is not required for remote viewing, that is done over the LAN/WAN.
With of course the correct software and phone. IPhone and Blackberry being the most supported.
Cameras need to be specific for the viewing required, for definition of the subject and for the prevailing light conditions. supplemental lighting may be required.
The larger Hard Drive the more data stored, although 12 Frames Per Second is the best in most cases. The human eye cannot really see more than that anyway. So a 500Gig would suffice for a 4 camera domestic situation. On larger multi camera systems I have fitted 4 Terrabites in the past. Expensive to say the least.
Try to avoid cameras with Infra reds in the casing, you get reflection issues and spiders like the atmosphere. A seperate ring and or lighting device is better.
Most DVR`s are now multi functional, but avoid anything under £300 IMHO. That is for a 4 way (Channel ) unit.
Movement or PTZ as it is known (Pan Tilt Zoom) is an extra. It requires more cable and a more expensive camera as it needs to be motor driven.
Also watch out for the protocals needed some DVR`s cannot control some/all cameras, a seperate keyboard is needed.
A decent DVR will allow electronic zoom and even "panning" of the available picture, but obviously not the same as true PTZ.
A good idea of what you need is a basis for a start of the design of the system.
Something like this will assist,
http://download.cnet.com/CCTV-Design-Tool/3000-2078_4-10814324.html
It is far better to work out than buy and find it does not do the job.
Facial recognition or ANPR ( Auto Number Plate Recognition) are the major criteria now days. A cheap camera and DVR will NOT be up to this.
This is really where you get what you pay for.
I hope this has helped.