Built mine 25 years back. Sunk a couple of 8" x 10' I beams from the scrap yard in about 4yds of concrete on each side, then laid the field stone around them. Welded some square tubing on the I beam, which holds the gate hinges ( 3 points on each ). Built the gates out of square tubing and some flat bar for the curved part. Gates are 10' wide, each. You can get by with a single 12' gate IF your entry and driveway are STRAIGHT.....mine aren't, and sometimes 20' is a tight fit with a long trailer. Recently had a tractor/trailer come deliver something, and he had a 48' trailer.....barely made it !
Used Genie brand linear actuator type openers at first.....complete pcs of junk, they don't even make them anymore. Any static electricity would pop the circuit boards in them at $75/ea.
Later went with a pair of OSCO brand openers ....GREAT opener....100% mechanical switching, not an integrated circuit on it. It's the "arm" type opener, using a 1/2hp motor and gear reduction box. Can't recommend them highly enough. Virtually no problems in 20 years.
For power, I ran a couple of #6 hots, 1 #6 neutral and a ground, a total of 900' , and it runs the gates with no problem + a security light on a motion detector. You CAN also run control wiring that far, all it takes is a couple #14, and some phone wire if you want a speaker. I didn't, but a buddy of mine just did over a longer distance than that. I used a subsoiler, then went back over it with a 'middle buster' plow to open it up more....I ran it all in PVC conduit just for protection, as it's only about 12" deep...but I ran down thru the woods where nothing ever disturbs it either. I also put a "pull box" ever couple hundred feet, turning a PVC 90 up, and into a PVC box, then back out to the next one.
As for getting under a drive, get a backhoe to come dig a hole on one side, then it can push a capped pc of 1-2" steel pipe under the driveway. Unscrew the cap, and you have an in place conduit. Water company does it all the time to put a meter on one side of a road where the supply line is on the other.