You probably won't believe me because of your inexperience with drop bars but because you're 6' 3" you really require HUGE amounts of saddle to bar drop to be comfortable on a road bike. It's counterintuitive and you won't believe it until you see and experience it yourself, but you need around 17 or 19 cm of bar drop. Having a low bar takes weight off your arms. I know you, like myself many other have done, will do everything except this first because you can't and won't believe it. It's the truth though.
It's good to have your center of gravity low on the bike.
Good climbing geometry also features steep headtubes, seat tubes, and low amounts of fork offset - basically like a professional race bike.