Hi unkleE,
First, congratulations on the purchase of your new Mac Mini! They are great machines.
To answer your question about transferring selected applications via MigrationsAssistant, it looks like it's all or nothing I'm afraid. This is according to the article how to move content to a new Mac. Also I attached a photo as well. I'm not aware off the top of my head of a third party migration assistant utility to transfer selected applications but others might be able to help on this.
This photo as you can see, there is a little triangle next to the user account and computer and network settings but not applications.

One third party application that can help determine what applications you have that are 64 bit as Catalina drops support for 32 bit applications is called Go64. It will list all your applications and provide upgrade paths for those applications that are 32 bit. It also has the ability to delete applications that you no longer use as well.
I hope this helps.