When creating a kubernetes deployment I set .spec.replicas to my minimum desired number of replicas. Then I create a horizontal pod autoscaler with minimum and maximum replicas.
The easiest way to do the next deployment is to use this same lower bound. When combining it with autoscaling should I set replicas to the minimum desired as used before or should I get the current number of replicas and start from there? This would involve an extra roundtrip to the api, so if it's not needed would be preferable.
There are two interpretations of your question:
1. You have an existing Deployment object and you want to update it - "deploy new version of your app".
In this case you don't need to change either replicas in Deployment object (it's managed by horizontal pod autoscaler) or horizontal pod autoscaler configuration. It will work out of the box. It's enough to change the important bits of deployment spec.
See rolling update documentation for more details.
2. You have an existing Deployment object and you want to create second one with the same application
If you create a separate application it may have a different load characteristics, so it's probably that the desired number of replicas will be different. In any case HPA will adjust it relatively quickly, so IMO setting initial number of replicas to the same number is not needed.