I prefer a completely different action from the dog when I run with him (or especially running with two dogs).
I do not want a loose leash when we run, it can be a trip hazard if the leash goes too slack (trip hazard for both me and the dog). I also want him out in front of me so we are narrow on the trail or path and I have good visibility of him to watch for signs of fatigue. I don't let him drag me along, but I want the leash (I hold the leash in hand) taut with just enough give for the slight movement of my arm not to tug on him.
When we walk, I let him be in front or beside me (so long as the leash has slack in it) and he can stop and sniff or pee leisurely (walks are for him to enjoy, running is for exercise). When first teaching loose leash walking, it will be a lot easier if the dog is a little bit tired out. So my opinion is to go ahead and run for a bit (maybe start at 1 mile with him running on dirt or grass) and then do a walking training session.
I teach loose leash walking in my driveway first- spending half a day (I'm not kidding) going up and down the driveway turning randomly so the dog gets used to tagging along next to me and learns to watch me for movement cues. I don't tug the dog along, I just turn and if he hits the end of the leash on his own, he'll figure it out. If he sees me turn and doesn't hit the end of the leash (by also turning), then he is getting the idea and gets praised. Once the dog has the idea, I will use treats to reward but I don't use them much for loose leash walking because I don't like the "lure" effect it has (dog follows the treat, not me).
I'm guessing he's a medium sized dog. I would say that at about 1 year old, shorter runs of up to 2 miles on dirt or grass are fine. Then slowly build up so that he can run the full distance with you by aged about 18 months at which time he should be full grown. He should have no trouble at all running 5-6 miles at a steady pace once conditioned to it. Keep him off concrete, asphalt is okay. Watch for debris like broken glass and avoid gravel paths (ouch for his poor feet). Check his paw pads after a run and remember that if he's pulling hard, he could tear up his paw pads and need a few days of rest. Learn signs of heat illness and remember that dogs overheat much more easily than people.
I used to run up to about 9 miles with my dog, with more typical runs being 3-5 miles. 5 miles was perfect for him to be just tired enough to be calm but not so tired he would start to slow down while running in mild or cold temps. (We never run in temps over about 75 degrees or maybe 80 degrees if there is a good breeze and the path is shaded and has water stops)
Edit to add:
I do NOT like the head harnesses at all and more so for running-- if you trip and jerk the leash, you can seriously injure your dog's neck. Same danger if the dog darts at a squirrel or you have to haul hard on the leash when some idiot driver fails to see you. Some of them are also bad about rubbing the nose and eye area painfully. The only head harness that might be okay is the Newtrix because it attaches on the back of the head and uses a different mechanism to discourage pulling. I still wouldn't run with it though, but I think its decent for walking.
the front attach harnesses are safe enough, but like Tofu_pup says, are a management tool (meaning, quit using it and the dog goes back to pulling unless you also incorporate plenty of training)