Start off by drawing a diagram of your house. Then walk around and see what views you need. That will give you an idea of how many cameras you need. Wired cameras are best, imo. You will have no interference issues, but wireless cameras are MUCH easier to install. You will still need to run power to the wireless cameras.
For outside be sure and get infrared cameras. They have IR transmitters so the cameras can see at night.
You can buy kits that include cameras and DVRs. You can hook those up to your TV, and network them so you can see on your smart phone. Some kits are self contained. Meaning you get a monitor with the kit and even some with a built in DVR.
Be careful and really research the system. Some are only viewable on your smart phone via SKYPE, and you can only see one camera and have to maintain an active computer connection.
We have a Swann 16 channel HD. I don't remember the model number but it was a bit spendy. Like most things you get what you pay for. It came highly recommended and after doing my own research I went ahead and picked it up. I am pleased with the unit, not the support from the company. They don't respond to email, and rarely answer there phone. The unit works like a champ, except for the default DDNS (so you can view it from the internet). The default DDNS is through Swann and only works sometimes. Your options to remedy this are use someone else for DDNS or a static IP. We upgraded our internet to a static IP and this fixed my only issue with the system.
The system we replaced was ok, but after an incident when we reviewed the recording it was just not good enough to do much with. So whatever unit you get, make sure the camera and recording is decent quality, HD preferred.
If you are willing to build your own box, Acti has good software and cameras. You can get a lot of camera and even an old computer will power their software giving you full control remotely, the ability to program detection, blackouts areas, etc.
I can very close to picking up a wired 4 camera system with DVR from radio shack for $400. I think it could handle more cameras but came with 4. 30 day memory IIRC, but that may have been total recording time(so 1/4 of that running 4 cameras).
Don't think it was set up for remote viewing online but with my Internet options I don't really look in to that stuff.