Actually, the fastest way to accelerate is probably to stand on the pedals, but that may only sometimes be the most efficient way. I believe you're over-thinking it. Find the best fitting, best equipped bike you can within your $300 budget and enjoy the ride. When people ask if $300 is your budget for shifters or the whole bike, they're talking about Di2 (electronic) or "brifters" (indexed shifters integrated into the brake levers). Most other shifters aren't quite so pricey. The type of bike you select (actually, the handlebars) will determine what your shifter options are.