If you are redesigning a little at a time then I use internal sources for the cabling. but if you are doing a larger job all at once then it is better to get an outside source to do the cabling unless your internal source thinks they can handle the job. Does the internal source have the tools to test the cabling? I don’t mean just continuity testing. They need to do a full load test on the cable to show full compatibility with the cable standard being put in place. I would use Cat6 if these servers are going to run all gigabit but cat5e will work fine but is pushing the limits of the cable. See the difference here:
As far as layout, that depends on your setup. Do you have a core switch that the servers are connecting back to? If so then go fiber from there to a Gigabit switch in the rack and hook all servers to that. The link back to the core switch would need to be 10 Gigabit if the servers are high volume servers. It depends on how many servers you have too. You could patch panel them from the rack back to another patch panel by the core switch, then from there to the core switch. But that depends on how far they are from the core switch. And you would need Gigabit ports on the switch for each server.