I'm adding a Synology DS 1513+ NAS to a small business network. The NAS has four ethernet ports for data transfer.
The current network configuration has a modem in bridge mode, hooked up to a consumer grade wireless router, hooked up in turn to a 16-port switch. Some additional machines are hooked up directly to the router and bypass the switch.
Is there any reason to split those ethernet cables across the devices? That is, will I get better performance with all of the cables going from the NAS to the switch, or would it be better to have two go to the switch and two go to the router?
D. None of the above.
Network link saturation is rarely the cause of performance problems, in my experience. Additionally, it sounds like you're trying to solve a problem that you don't even know exists, which is a bit like tilting at windmills.
That model has 1Gbe Ethernet ports, I'm skeptical of the idea that a single 1Gbe link is going to be saturated by the usage that's typical in a small business. My suggestion would be to connect the NAS to the switch and put it through it's paces by allowing users to access the data on it over a few days and monitor the link utilization (assuming you have a managed switch that will allow you to monitor that switch port).
Additionally, if you find that you need to aggregate two or more ports on the NAS for performance or fault tolerance reasons, simply plugging those ports into the switch or to the switch and router isn't the method of doing that and is a recipe for creating network problems. What you need to look into is Link Aggregation, which that model may or may not support.
https://www.synology.com/en-global/knowledgebase/tutorials/525
workstations & NAS > switch > router
. It's better, easier, and would offer the most local performance (all port speeds being equal)