The new H320 APs require minimum firmware version: 10.0 (+AP bundle update) or 10.1 for native inclusion.
The new R510 APs require minimum firmware version: 9.13.
Your H500 (assume you mean this as there isn't an H300 AP) will work on firmware 9.10 to 10.1
The R500 will work on firmware 9.8 to 10.4.
Therefore it appears that 10.1 is the 'sweet-spot' firmware version that will allow you to run all AP models simultaneously. However you will not be able to upgrade beyond 10.1 unless you replace the legacy AP models as noted above.
Please ensure you thoroughly check the relevant read-me notes before upgrading to ensure you take the correct upgrade path, etc.
I hope the above information helps. Please note, you will not be able to access firmware and documenation without an active support contract. I recommend you speak to your Ruckus partner to progress this.