To limit the abilities of a user group you will need to assign Roles to that group. Roles are how WordPress defines permissions. If you want to limit what a user or group of users do you need to specify this with a role. There no magically formula that going to figure this out for you. You just need to find a plugin for assigning the roles you want.
To automatically select a category for each user you would have to determine what criteria too use to select the default category. In WordPress Categories and Tags are known as taxonomy. There is nothing in WordPress that will select a starting taxonomy based on a given set of criteria. You can search the plugins to see if you can find one. WordPress doesn’t possess any form of AI. It not going to figure out what you want .
You can limit what a user can do by using Roles. You can’t have WordPress decide on a given taxonomy based on some unknown criteria.