I've flown most of the major airlines over the years. Delta is no worse than any of them. Hopefully you are on a non-stop flight. If you do have to connect (change planes) for a fearful flyer, I would recommend NOT using Atlanta as your connection point or leave at least 2 hours to connect. Atlanta is a large, crowded airport (and for those of us with warped senses of humor, DELTA is an acronym for Delay Everyone's Luggage Through Atlanta), and if you're not familiar with it, you want to leave time for delays and finding you way to the next gate (though the underground train between terminals can be fun). Delta also connects through Minneapolis which is a large airport and can be a hike between terminals so I would leave additional time when connecting there as well. I haven't been through any other Delta Hub.
If the flight has wifi, you can use the Delta smartphone app for free, and the last time I flew the app had a mapping function to show where the aircraft is, which was kind of cool.
Generally I don't pay for wifi on a flight...it is rather expensive. I tend to preload a movie or two on my tablet or smartphone.
If you wind up going with United, SOME aircraft have an on-board audio channel that lets you listen in to your flight's communication with air traffic controllers which is cool.
Happy travels.