I assume you’re after Gigabit speeds, and your router isn’t Gigabit? If so the simplest option is to get hold of a cheap Gigabit switch. Connect the router, the PC and the NAS to the Gigabit switch and you'll have permanent Gigabit speeds without having to mess with any settings.
For your original query it’s really just a matter of doing things in the correct order.
With your PC configured to get its IP address automatically connect everything together via your router. This will allow both devices to obtain IP addresses from the router’s DHCP server.
There should be instructions with the NAS that’ll tell you how to access the configuration pages. With any luck there’ll be an option to set a static IP address. Configure it with an IP address in the same subnet as the dynamic IP issued by the router. Make sure you can still access the NAS using the new IP address.
Now configure Windows to use a static IP address in the same subnet. Again make sure you can still access the NAS.
Finally connect the PC directly to the NAS. With any luck you’ll still be able to access it.
When you’re done connect them back together via the router and revert them both back to dynamic IPs.