If you will keep the onsite management, I recommend setting up a weekly performance review once a week. That way, any issues that come up can be addressed.
Or, you can communicate with them on an "as-needed" basis, which is what I do for my 12-units. I ask the management company to reach out for any expense over $500 and whenever there is a vacancy so we can determine a plan of action in regards to what repairs/updates to make and how much to charge in rent. But once I get more than 30 to 40 units, I plan on setting up a weekly call.
If your goal is to be 100% passive, I recommend researching apartment syndicators and investing in their deals.
@Evan File Biggest situation which you must resolve is never letting your eyes get off the ball. For smaller properties, your PM is, probably, not going to be the best and brightest especially if they've been in the same position for 10 years.
You will need to make sure weekly, monthly, quarterly and annuals goals are met, vacancy is kept to a minimum by either increasing your renewal rate or always marketing, keeping a tight watch on all R&M/capex as well as managing your cash position.
This all sounds daunting but once you have systems and policies in place, it isn't too bad.
@Evan File I would review the current property management agreement to see which duties and services are included.
In addition, I would investigate if the on-site manager is full-time or is only on-site for a specified period of the week. With a full-service property management company, you should be focused on establishing an annual budget and periodic update calls to track the progress.
On larger properties, outside of performance calls, owner's usually get involved if there is a big bust in the budget (to alter the business plan if needed), capital expenditures are going to be more than estimated (find ways to cut costs if possible), or leasing strategies need to be adjusted to keep up with other competitive properties (example: providing concessions on new leases or renewals).
@Evan File Think about your fourplex. How active have you been since you found it? How much time you put into it? Property manager is hired help. He or she needs an incentive to perform well. Hopefully their fee is a percentage of the rents collected! Additionally, at the end of the day, as @Omar Khan said, you will have to set the systems in place. Until then, plan to spend a lot of time at the property. I'd recommend as @Theo Hicks said to stick to a weekly report from your PM and then calls on as needed basis.
Before you jump into this investment, ensure that the numbers work and the overall investment makes sense = low vacancy, demand is high, town population is on the rise, jobs are available and accessible, etc.
Best of luck!