I am unsure what you mean by unstructured. However, I have been with Owners from the beginning phases of their companies and have learned a thing or two about what was successful for them. First off, I would hope that the "Corporate" office have a strong accountant familiar with property management. To answer your question, I would absolutely want your property manager to be well versed in all facets of the business - should handle all the rent collection, and I would take it a step forward and set up so that from the property the checks and money orders are scanned straight to the bank. There is less chance of a check being misplaced or lost or stolen. It is also nice if your property management software system accepts and integrates online payments, but when the company is small, maybe you will choose to delay this.
Your Property Manager will be a "jack of all trades" when your company is small, so he/she should handle accounts payable, too, so, just as Nicholas said expenses can be tracked and vendor invoices submitted through the software system. I do not recommend using Quickbooks - I like actual pm software so reports can be generated and emailed directly to investors.
Your Property Manager should also be able to bid out all your monthly contracts and capital projects and submit them to you/Corporate for final selection. As far as maintenance expenses, these can also be tracked through software or you can set up an inventory list in excel for the PM and Maintenance Supervisor/Tech to use to track supplies. You will want credit accounts for local vendors, like Home Depot (HD SUPPLY), Wilmar, Johnstone, etc. to obtain materials for your onsite team to use for turnover completion and repairs. You can always implement a limit on what they can charge/order, plus limit who controls the account so that purchases must be approved. Most vendors are happy to email or fax orders to you for approval as well, so you know what is being ordered and can call the property to ask why. For example, in my experience water heaters seem to go out in 3s. I always like to have one extra in inventory but I never have 3, so if I had a need to order 3, you would see the email and could ask me what is going on if I have not already informed you of the issue.