Custom Post Type/Category-Archives Page for Custom Taxonomies

I'm working with a couple custom post types. I've been able to customize the display for individual posts with single-post_type.php created using Custompress plugin, but I'd also like to edit Category/tag page displays for custom taxonomies as well. Customizations I'd like include:

Remove "published by", remove the date, remove the avatar, and add a couple custom fields.

If I can get pointed to the base page for archives?/categories? ( like single.php is to single-post-type.php) I could probably figure it out.... though any above and beyond guidance would be greatly appreciated.

Hope that makes sense, I'm not very fluent in WP language.