We own a carpet cleaning company. We just replaced carpet in our home last month. My husband knows a lot about carpet fibers and he says stay away from polyester. Typically polyester will be cheaper and the warranty is small. It is also not good in high traffic areas as after just a short time the fibers won't stand up anymore.
He highly suggests getting nylon. That is what we got. It was a bit more money, but the warranty is a lot longer and he says it is better quality.
As far as who you go with, you really want good installers. That is key. They should not use a knee kicker to install the carpet, they MUST use a power stretcher. We have bought carpet from Home Depot twice and have been very pleased with them. They locally contract out the install, but it's their name on the line, so they typically get the best, imo. Should you decide to go with someone smaller, I would def call and ask how they install.