Best way to find out and set application resource limits/request on kubernetes
I usually start my pods with no limits nor resources set. Then I leave them running for a bit under normal load to collect metrics on resource consumption.
I then set memory and CPU requests to +10% of the max consumption I got in the test period and limits to +25% of the requests.
This is just an example strategy, as there is no one size fits all approach for this.
The VerticalPodAutoScaler is more about making sure that a Pod can run. So it starts it low and doubles memory each time it gets OOMKilled. This can potentially lead to a Pod hogging resource. It is also limited as it doesn't take account of under-performance. If your app is under-resourced it might still respond but not respond in a timeframe you consider acceptable.
I think you are taking a good approach as you are looking at the application under load and assessing what it needs to perform as you want it to. I doubt I can suggest any tools you aren't already aware of but if it helps there is some more discussion in How to set the right cpu millicores for a container? and the threads that link from it