Welcome. Before you purchase a full set of gear, be aware many would suggest taking time to get acquainted with more options first.
For example, there's a decent chance the BCD you encounter will be a jacket style BCD. You ought to learn about the BP/W alternative, not because it's better for everyone, but because it's a viable option.
Similarly, a good regulator may cost several hundred dollars, but it does not need to be labeled 'titanium' and priced around $1,500+. But you may want a brand that a local dive shop services, because it's recommended to get them serviced periodically.
For dive computers, some thought should go into wrist vs. console unit, air-integrated vs. not, and where you see your diving going in the future, if practical.
Take each main piece of gear - mask, BCD, regulator, fins and dive computer (I'll skip boots; that's not quite is pivotal), and do some digging on ScubaBoard, read some threads, and see what looks good to you.
When you say 'wreck diver,' do you mean fin around the exterior, or do you want to do penetrations inside them? Do you just plan to dive some wrecks amongst the coral reef diving many do, or do you plan to take dive trips dedicated to wreck diving? What is it about wrecks that draws you?