What software would I use to create amazing company logos and business cards?

First develop your design skills, understand typography, color relationships, negative and positive space, etc. etc. then worry about the software. Software is a tool, if you don't have the knowledge and skills, it won't make a difference.

The software is irrelevant, if you haven't got the skills you can't produce "amazing" company logos and business cards.

PhotoShop, or Gimp (which is a freeware clone of PhotoShop) are what professionals use, but how "amazing" they look depends on the person doing the creating. Can you do them on paper? If so, you may have the artistic talent needed to make them in an app. Then you simply need the app and learn how to use it.

Photoshop.

cooltext.com

Paint?