I've never rented one out but I wouldn't be afraid of the learning curve. They look really simple to use but then I've driven tractors with buckets so YMMV. As for renting versus hiring, it would have to be a pretty big cost savings for me to rent a skid and do it myself for a few reasons.
Having seen pictures of your front yard, staging that much road base and removed dirt is going to take up a lot of real estate with both there at the same time. If it isn't, then you have to figure in scheduling and waiting for the road base into your rental or schedule two different rentals. Also, living on a contained plot of land, what are your plans for any extra road base materials you don't use? Then comes the joy of estimating it ahead of time. Do you order just enough, risk running short and having to schedule and pay for delivery of a tiny load or do you order extra and now have to figure out where to put it when not used. I would pay somewhat of a premium just to not have to worry about those things. But like everything, it really depends on your budget.
As for the damage protection insurance, I guess for me it would depend greatly on what it covers. I tend to self insure for things like this, but again, my budget and savings account may not be the same as yours. If you don't insure and it goes up in flames, will it put you out on the streets?