Back to your original question. If you are convinced that you want to be a trader on buy-side, meaning no hedge fund, no AM, no banks, then go for a prop trading internship. All of the interns at Citadel this summer got automatic invite to IMC superday, so even if you don't get a return you will land in a same level/better shop.
The cons of a prop trading internship is that very few people outside of this industry would want to hire you full time. Banks don't hire outside of their internship class; AM s have no idea what prop trading is, and unless you are at a top level shop, no hedge fund will even interview you.
The benefit of starting with a BB trading internship is that even if you don't have/ don't accept the return offer, all the props +AMs+hedge funds+some BBs would still want to hire you.