Thank you for your post.
To organize your contacts by Company, the primary sort would be Company name with Last Name being the secondary sort. You can also include First Name as the tertiary sort.
If you have a drop-down list by Company, you may want to consider a calculation field that displays the Company, First Name and Last Name. That way, you can select the specific contact at a specific company.
Let me know if you need clarification for any of the above steps.