Final answer:
The organization should purchase a multi-user license to provide software access for an unlimited number of users across various installation methods.
Step-by-step explanation:
If an organization intends to provide access to software for as many users as it wants, with the flexibility of individual installations, network access, or internet passwords, the appropriate type of license to purchase is a multi-user license. A single-user license would be limited to one person, a trial version would only be temporary and typically has limited features, and open-source software, while it may allow for unlimited users, might not meet the organization's specific needs or preferences if they are considering a licensed software.