Its going to be difficult to say what is reasonable for your area when you specify "quality" but want to cover "rural or residential." And to have a single price for weekly/biweekly is not going to work. Most likely a biweekly service would be at least 50% more than weekly. And to think of this as a per acre price that might be appropriate generally for all properties is not going to work.
I do rural mowing. What is "quality" for what I do would not be deemed quality for in-town residences (but there would be no in-town properties in my area that were an acre in size). Rural can mean working farms with chickens running free and scratching holes in the lawn for their dirt baths and former fields that are rough from furrows left by plows, or multi-million dollar estates that are groomed to perfection and as smooth as the greens at a golf course.
I see multi-acre properties that have a house and garage in the center and not a single tree or bush within the fence boundary, and others that have all manner of obstructions to slow mowing.
I suggest that you develop a very good sense of the actual time needed to mow the various property types to the satisfaction of the owners, and then treat and quote each property individually based on the time required and what you consider a reasonably hourly rate. Because these will be unique properties, until you have experience so you are confident in your estimates of times that will be required, do not be afraid to give a quote covering the first one or two mowings with the understanding that the price may be adjusted up or down after that (probably with two weeks notice so they can find someone else to do the work if they do not like the revised quote).
As for figuring out what kind of dollar amount to apply to the estimate of hours, I think a good starting point is to take whatever number you think is reasonable compensation for yourself (and when figuring that do not forget to include the 15.3% federal self-employment taxes, and any comparable state self employment tax, that you will be paying personally in addition to your estimated income tax payments). I figure that my equipment earns as much as my body so add an amount equal to the figure you deem reasonable for your personal compensation to cover equipment compensation. Depending on your local fuel prices, consider adding the cost of fuel. When doing rural mowing you will not have compact routes, so include travel time when estimating the hours you will spend on a property.
You have to figure out how you are going to include payment to cover administrative time, whether that is someone else who keeps the books, answers the phone, handles payments, or if you are doing it yourself. And you need to include costs for overhead such as driving to properties and analyzing them so you can give accurate quotes, and allowing for many of those trips to give quotes not leading to paying work, and for overhead for such mundane details as shopping for new equipment. (Do not add an amount for time you spend on LawnSite -- that is on you personally.)
And you need to include in the quote enough to cover costs for insurance, business licenses, etc. It all becomes pretty complicated
