... would like to buy a DVR and security cameras. Question, if I buy HD 720p or 1080p cameras, can they HD picture be played back/downloaded from a standard DVR or do I have to buy a specific DVR for those types of cameras?
Let's face it, you are not buying security. You are buying equipment. As for your question, you don't even own the equipment after you buy it. There is a good chance that your recording is compatible with any player you happen to have, but the player refuses to work in your continent, or the recording has a DRM bit set, or other trivial matter. You have to get the dealer to spell out all such restrictions before you buy the equipment.