I am not trying to be facetious, but like you I have a quarter-mile long driveway from the front gate to the house (there's another quarter-mile of county road between the turn-off any the front gate). I've tried wired and wireless systems, but the best, most reliable, non-falsing, alarm system I have ever had has been a dog.
The dog would alert me that someone was coming at least three minutes before I could hear their tires on the gravel and I could hear the noise of the tires well before the electronic alarm detected them passing over the cattle guard. Plus, the dog would come find me where ever I was on the property even if I was out of earshot of the electronic alarm.
Plus, if you train it right, a dog will give you unconditional love and you can't get that from an electronic device - although I read an article yesterday saying that there now robotic prostitutes that will try.