Use the 4-way neck machine, it's probably designed to increase neck size if used properly.
There are two other things that you should do as well if you are serious about neck size.
Buy a neck harness. Iron Mind Enterprises has the best one on the market. Elite Fitness also sells one. You can work your neck from evey angle adding plates as you move along.
I like the neck bridge. Being a former grappler I could see the benefit (in size and strength) of bridging. Do both forward (on your forehead) and then backward, on the back of your head. Do this on a mat, or a pillow if a mat is not available. Start out by bridging for only :15 seconds. Work up to 1:00 or so. As you get better at it you can move around while in the bridge, rolling in small subtle motions.
The neck is used to doing quite a lot of movement during the day. Therefore, I would train the neck with high reps three times per week. In a specialization program I would train it from each of the four directions three sets each for a total of 12 sets. That may seem like a lot, however you are not going to come even close to failure. Work in the 15 to 20 rep range. Change up between the machine the neck harness and bridging.
Again, that would be a specialization program only. Once I brought my neck up to the size I wanted it I reduced this program to include only three sets three times per week, and sometimes only twice per week.
I brought my neck up from 14" to it's current measurement of 17". Not huge, but for my body weight, fat percentage etc. it's not bad.