My opinions, and most people disagree with me:
1st priority: exposure suit. It's personal equipment. It's all over your skin. It's like underwear, and I won't wear other people's underwear. Also, like a mask, fit is everything. Buy it locally. Try on a lot of them and buy the one that fits right. Don't try them on locally, then buy online. That's not ethical to use stores that carry stock as a free fitting service.
2nd priority (and here is where my opinion differs from many): regulator. One, it's also personal. People put them in their mouths and breath into them. I'm happy to swap spit with my wife, and I would with my girlfriend if I could find one, but I avoid sharing toothbrushes with strangers even if they are washed thoroughly. In an emergency, sure, no problem. But not on a regular basis with a wide variety of who knows who. Two, It's most important that you know that your reg is in proper working order and that it has been properly cared for. Most rental regs are kept well serviced, but not all are. It's a crap shoot to rent.
BCs vary quite a bit not only in general styles, but also between models of the same style. The differences can only be felt properly in the water, not in a store. Rent a bunch of different kinds before buying and try them in the water. It's the only way you'll get to see what you like. (And you may have to look long and hard to find a place to try out a BP/W, but I think it may be worth it to you.) In contrast, buying any reputable reg, even without trying before buying, will work out for you for a long time.