It's still possible to leverage a third party carrier contract even while using your own FC. Aggregators, consultants, and resellers provide various benefits.
In addition to setting up your FC, or at minimum shortly thereafter, you want to start establishing your own contracts with a national carrier. Getting the first one done is the hardest part.
The reason is you will always achieve the best cost structures for contracts optimized to your SKU and shipping profiles. It is virtually impossible to do so otherwise.
A general rule of thumb: There are 4 "nationals"—USPS, UPS, FedEx, and DHL. USPS is best at very small parcel sizes; UPS is best at ground and commercial shipping; FedEx is best at fast methods and SLAs; and DHL is best at combining international shipping options. While all are a valid first carrier, pick the one that best fits your business at this stage.