Cogent and Qwest are bandwidth providers. Those are the backbones providers that will give life to your server ;-). There are people out there that do not like Cogent. But let me assure you we have been using them for over 2 years now without a single problem.
Now it is possible to have problems, but that really has to do with the colo and provider you sign up with. Not everyone provider will use nice networking equipment and have the skills to setup everything correctly.
So don't be affraid to use a Cogent provider, because you really can't beat the price and service if it's done right....
Well that is a neverending subject. Fact is that Cogent (cannot say anything about qwest, no experience) DOES have problems now and then but that's ok. Cogent is 25% or less of what ohter providers cost. Also most people use Cogent in a MULTIHOMED connection so if it has problems the f.e. BGP4 will route through the other provider.