its great that you are starting to use adobe Illustrator!
for creating logos, you are already on the right track. If you want to use your logos to create business cards or mockup designs using your logos, it is best using Photoshop if you have it.
You can first save you logo from illustrator either in an eps or pdf format and transfer it to Photoshop. the beauty of it is that your eps file will adapt to any size in Photoshop depending on the size of your file.
as you can see the logo are both crisp even if placed in documents with a great size difference.
Photoshop is just a better program to create mockups in general since all elements such as images and fonts can be easily edited.
I hope this answers your question, have fun!