I do want a large PC. I'm actually working on my own homebrew centaur race right now. Centaur is nice because the human-sized upper body gets around the whole large-sized weapon issue.
My biggest concern about playing a large-sized character (and, as a DM, allowing large-sized characters) is, unlikely though it may seem, survivability.
Let's look at a large creature honestly. If there is a party and only one of the PCs is large, most foes will see the big brute as the big threat (unless obvious mage is obvious) and try to take it down before it lays the hurt on them. Most rational humanoid enemies would, very reasonably, focus-fire the large PC to death. At early levels this would be painfully easy to do since the large PC would likely squeeze only one extra hp per level out of her racial Constitution bump.
A large PC is a big bull's-eye who has even less potential to hide than normal PCs. I would be very worried about that.
Yes, the target and hide issues were something that I brought up, but others seem to think those less significant.
With a centaur, have you considered giving it a back-kick maybe as a reaction or considered if you would let other PCs mount it?