My DMC buddy, who I also did rescue training with, is 6'7" 240. He's a triathlete so well proportioned, not overweight at all.
He uses off the rack stuff, including a shorty and 5 ml, although I've noticed that his BC doesn't really fit properly and he usually wears his shorty. When he needs to wear a heavier wetsuit, he has the 5 ml, but has been reluctant to buy a 7ml or drysuit,yet, due to the hassles involved. I believe he'll need custom for those. However, he'll need to,soon,because of the fact that where we dive ( AZ/CA) really requires it.
He is looking at a BP/ wing but he's gotten by for 10 years, all the way up through DM with somewhat crappy,off the shelf gear.
Now, he is the type of person who makes do with what he has, drives an old, beat up car and waits until something is intolerable before its replaced. My point is, that OP is likely to be able to get through OW class before needing to buy everything, except perhaps his wetsuit or a 1ml skin.
BTW, I'm 5'1", somewhat disabled. It's quite a comical site, I'm sure, to see my buddy and I working together and testing on things such as rescue and especially the gear exchange.
I was never so proud of myself as when I beat him in the endurance swim and was then able to drag him ashore for the rescue portion of the DM test just after our swim test!