I'm considering getting a NAS with a 1GbE port and a 2.5GbE port. My incoming internet speed is 1Gb, but my router, an AT&T BGW320, has a LAN port that can accommodate up to 5GbE. Forgive my ignorance, but if I connected the NAS to that port on the router, would the LAN speed be up to 2.5Gbe between the NAS and the router, or would it somehow be limited to the speed of the incoming internet?
For anything except the most demanding commercial applications, even 2.5GBps is overkill, and the speed of your connection to the outside world has no effect on the speed of your internal network which is only governed by the maximum throughput of your ports and wiring, ie you could have a 5GBps internal network and "only" a 1GBps internet connection - downloading and uploading from the internet would be limited by that 1GBps cap, but if you were transferring files across your internal network (ie from computer to NAS, NAS to streaming box etc.) they could go at a full 5GBps provided that all the hardware connected supported it.
The reason I say 2.5GBps is overkill is that even the most demanding of data streaming only uses a fraction of even a 1GBps connection, so unless you're planning to have a dozen or more devices simultaneously streaming/transferring from your NAS, 1GBps is plenty. Just to put it in numbers a bit:
Device/standard - maximum transfer speed in Mbps (megabits per second)
5Gbps ethernet - 5000Mbps (1Gbps = 1000Mbps)
USB-C 3.0 - 5000Mbps (never had anything close to this, the fastest I've seen on my computer is about 1600 for a SSD to SSD copy)
2.5Gbps ethernet - 2500Mbps
1.0Gbps ethernet - 1000Mbps
USB 2.0 - 480Mbps
UHD 4K Blu-Ray - 128Mbps
1080p Blu-Ray - 40Mbps
Netflix 4K streaming - 16Mbps
192/24 4.0 Quad (Quadio) - 12Mbps
96/24 5.1 FLAC - 8Mbps
48/24 Dolby TrueHD Atmos - 8Mbps
192/24 Stereo FLAC - 5Mbps
Netflix 1080p streaming - 5Mpbs
48/24 5.1 FLAC - 4Mbps
96/24 Stereo FLAC - 3Mbps
48/24 Stereo FLAC - 1.6Mbps
16/44.1 Stereo WAV 1.4Mbps
16.44.1 Stereo FLAC 0.8Mbps
16/48 DD+ Streaming Atmos (Apple Music) - 0.7Mbps
320kbps stereo mp3 - 0.32Mbps
So as you can see, even the most demanding of these applications (4K BluRay) only uses a little over 10% of a 1 gigabit connection - I've ripped many 4K Blu-Rays to my NAS (10+ year old HP MicroServer with a 1Gbps wired Ethernet port) and I've never had as much as one playback problem caused by the network port. If you can get 2.5Gbps or 5Gbps hardware for little or no extra cost (or if money isn't a consideration) on top of 1Gpbs then by all means but lower-bandwidth data will go through your pipe just the same whether the width of the pipe is 1, 2.5 or 5Gbps.