2.16, never use a 3.x, there are only some specific use cases I think for it that you would know if you needed it.
App Volumes 3.x was initially released for Horizon 7.x but the product was more compatible with the Horizon Cloud Platform and hence was moved exclusively to be used by Horizon Cloud on IBM Cloud (aka Horizon Cloud Hosted).
- At this point, App Volumes 3.x has been taken off the shelf to be revamped where the next Cloud variant of App Volumes will be on both Horizon Cloud (Hosted and Azure) platforms.
- All Horizon 7.x On-Prem deployments are to be accompanied only by the App Volumes 2.1x versions
Always ensure you validate the compatible versions of Horizon and App Volumes with the Interop Matrix - VMware Product Interoperability Matrices
If you play around with this, you will see compatibility only between the On-Prem Horizon 7.x and App Volumes 2.1x (3.x is not available)
Below shows Horizon 7.7 being compatible with App Volumes 2.13 to 2.16 (latest)
= which means you will need to upgrade your App Volumes to a Compatible version shown below (at least to a 2.13 version) before upgrading to Horizon 7.7.
Apart from the compatibility I would suggest either 2.15 or 2.16, not 2.13 or 2.14.
For as far as I can see now 2.16 seems to be your best bet, it works quite well with login times and application startup. Do keep in mind that there is still a "bug" with the manager if you upgrade it instead of doing a fresh install. After upgrading you cannot see appstacks anymore when going to Appvolumes --> Appstacks.
And IMHO 3.0 has been pushed out by marketing instead of engineering. They (WMware) wanted to show what could be possible with Appvolumes. I believe it is the word (or version) that you shall not mention when inside a VMware building