I'm signed up for the PADI Wreck Diver specialty. I had the same experience as the OP - a charter guide took me into the YO-257 and San Pedro, and entering through a window, floating up a staircase, and exiting to a different part of the ship was really fun. Unfortunately I don't think there are many wrecks here that really require Advanced Wreck training. I'd like to take the Advanced Wreck course just for knowledge and experience of using the equipment but the TDI shop here doesn't offer it. I already have most of the gear - assuming I wouldn't need my own tanks - and buying a single long hose and maybe an H-valve isn't that big of a deal.
I looked at PADI wreck-related courses, and also looked at TDI/SDI. The TDI/TDI website lists the Course Standards and Procedures (.pdf) for every course. The TDI 'Advanced' Wreck course requires the TSI 'Basic' course OR SIMILAR (including PADI Wreck specialty) as a prerequisite. The material *as indicated in SDI and PADI literature* is very, very similar. They are both basic introductions to wreck diving:
SDI Wreck Diver - SDI | TDI | ERDI
Wreck Diver | PADI
The equipment needed for PADI Wreck Diver specialty:
'...basic scuba equipment, plus a dive light, a slate, and a line and reel. Your PADI Instructor or local dive center staff may suggest other gear appropriate for wreck diving in your area.'
The TDI Advanced Wreck course is different. The requirements include alternate air source, long hose, lines, cutters, etc.
TDI Advanced Wreck Diver - SDI | TDI | ERDI
If you work with a local/independent instructor, you may be able to find that taking a basic Wreck Specialty course cost little more than going on dive charters for the same amount of dives, which reflects my experience.
I would skip strait to Tech 40 or Tech Apprentice (whatever agency you like). Those skills are pretty much universal for all your future diving, pick some deco and deco gas. Maybe your instructor can package up self reliant and wreck. Many instructors bundle Advanced Nitrox / Deco Procedures with Advanced Wreck because they go hand in hand. If you take the Padi wreck enjoy it and meet new like minded people! Good luck, I'd like to hear what you think after the class.
Billy