I would like to use DriveHQ for managing my personal files. I would also like to use it for managing files for two organizations I'm working with, which also involve other people.
Based on what you described, a group account is strongly recommended. With a group account, you can create/add/delete/manage sub-accounts; you can allocate storage space and download bytes to sub-users; you can share files / folders to sub-users and contact groups with different levels of access permission.
With 2 organizations, you might create 2 sub-groups for them; or at least create 2 sub-user accounts for them.
I would like to be able to use folder sync to my PC for both my personal files and files from the two orgnizations.
Yes it can be done via group shared folder. You cannot logon to multiple accounts at the same time; however you can access files on multiple accounts by using the (Group) Sharing feature. Files shared by other people to you are accessible in the special folder: \DriveHQ Share\
What is the best approach to take as far as creating accounts?
Again, recommending Group Account service.
What are the pros and cons of having other people involved in the organiztions use "sub-accounts" vs. creating their own DriveHQ accounts, and having the organization share with them? Are there different behaviors as far as folder sync etc. go?
The main difference is Manageability. With a group account, you have one master account to manage the whole group; you create accounts for them, assisting them if there is any logon / technical issue because the Group Admin account can fully manage and even logon as a sub-user account.
Sub-users never need to logon or order premium service. If the master account is a premium account, then all sub-accounts are also treated as premium account.