We were able to negotiate rates with Fedex without much trouble as a small business. They have graduated increments of discounts based on shipping volume. Their quota's aren't as high as you would think either.
We originally started out with a small discount that still ran a bit more the USPS. We let them know that we don't want to have to price shop our shipping. We let them know what our shipping volume was going to be. They renegotiated the rates with us and now use them exclusively for our domestic packages. (which is a large bulk of our orders) Our letters and international shipments still typically ship cheaper through USPS though.
As for who to talk to, we have a regional sales rep that we deal with. For a startup, you'd probably want to look into their small business program and get in touch with someone through there.
We have done no research with UPS at this point, but plan to at some point. For us, their prices were the higher of the three starting out, so we left them off the preliminary list.