Diving on wrecks - AOW is fine (
depth of wreck permitting), if you aren't going to attempt penetration; but a Wreck Diver course might add some appreciation and understanding to your dives (
vessel structure, history, composition etc).
Diving in wrecks - Wreck diver is the minimum training to enter a wreck (
overhead environment), even under very limited circumstances. A very basic wreck course (the PADI is very basic, but instructors provide more, or less, depending on quality) will help you attain good buoyancy/trim/propulsion which is critical, help you fine-tune your dive equipment for wrecks and teach you the rudiments of guideline use, visual communication and gas management. Other courses might go well beyond this, teaching critical contingency drills for lost guideline, lost buddy, silt-out (low/zero viz), entanglements etc.., as well as redundant air sources and more refined gas management.
Word of caution: Some dive operations will be content to take you into wrecks without formal training. This is a financial, not a safety orientated decision on their part. Without having done appropriate training, it is what we call a 'trust me dive'; the abdication of your responsibility for personal safety to the absolute trust of another diver (
who you may not even know well). If something went wrong (
and much can, inside a wreck) you might have to get out by yourself - and won't have the skills/knowledge/experience to do so. Without training, you are not properly informed of risks, therefore any decision you make, or advice you take, may be entirely flawed in reasoning. If nothing else, proper training informs you of the risks, so you can make accurate decisions about what is, or is not safe for you to attempt.
Some resources on wreck diving:
Silt Out! Wreck Danger! video
How to Evaluate a Potential Wreck Diving Course
Basic - Advanced Wreck Diving, Course Notes