often a separate NIC (ethernet PCIe card) is a good idea since many manufacturers are using *low budget* ethernet controllers on board.
such controllers leave much of the work (buffering, TCP checksums, ect) to the driver, in fact the operating system.
more advanced (and more expensive) controllers do this work in hardware on the PCIe card so leaving more CPU resources (and I/O operations) available to the operating system.
dual port cards (often used with servers) _can_ allow doubling the bandwidth - this is a feature called teaming which is provided by the respective driver (synchronizing the traffic from both lines).
however there are different configurations for teaming, some do only provide failover (if one line fails the second still works) and the adjecent NIC as well as the switch between both dual-NICs also has to support such a teaming - more precisely call it link aggregation.
so i would recomment to leave selecting all involved devices to a specialist or reading the respective product descriptions very attentively.