I've used (here in the U.S.) a powered airless sprayer for many years with excellent results. They're quite expensive to buy for a good one… perhaps as much as $2,000 (US) but they can be rented at most DIY stores for probably about $75 per day.
However, for that rental, a reasonably experienced painter can do most of a standard sized house in one or two days. A fence should be no problem for one day's rental, assuming you have everything prepped prior to the rental day.
Thing is, since they are "airless" (meaning the paint isn't powered out of the gun with compressed air but rather, with hydraulic action) there isn't very much overspray… in fact I can paint up to maybe 2 inches from door and window frames with no overspray. I carry a smaller 2 /12 to 4 inch brush to finish out the small strip left to the frames.
One thing to learn early on is not to have the pressure set up to high on the machine. To do so uses way to much paint. Additionally, don't skimp on the quality of the paint...