We already had regular stock fencing here when our donkeys arrived, and it's been working fine for them.
No experience with post and rail fences, but I' don't think a single rail would be enough to keep them within the boundaries of your property, but it might work as a subdivision?
Mine are on track grazing over the summer, and they have been very respectful of a single strand of electric fence (so my sheep can slip underneath), but their shelter has a slip rail gate, and if I only shut the top rail they'll get out under that in no time (not that I ever shut them in, the gate rails are there just in case of illness etc.)