In terms of ssids, what's the best way to setup a WiFi network across both 2.4 and 5 GHz?

All using the same ssid?
Separate ssids for 2.4 and 5?

This will be using 2 different access points, with separated channels on both frequencies.

I currently have separate ssids so I know when I'm connected to 5 GHz to ensure it's going to be quick for things like file transfers, video streaming etc.

My understanding is that to do the same SSID on 2.4Ghz and 5Ghz and have your devices connect to the correct channel based on their capabilities, your router needs to support "smart-connect" or Tri-band. Without this, your devices won't be automatically switched away from the 2.4Ghz channel to the 5Ghz channel if they support it.

I'm not sure if you can accomplish smart-connect / Tri-band with two separate routers, I would suspect not.

I think Matt's right - you need an access point capable of managing its clients across the two bands. I've used a few Ubiquiti AP's and they seem to manage it pretty well, for example.