This is a subject well covered many times, you could do a search and find many opinions. BUT you asked:
I would try these things first one at a time till you feel comfortable:
Stable Loads - By Torklift (I would have them but the dodge 1 ton SRW springs require drilling a hole through them, I am not up to it)
If that is not enough:
Bigwig Rear Sway Bar - By Hellwig(got one myself and it was a good investment, like the improved handling and less sway)
If these two items do not help enough, many people go with Timbrens or added spring leafs. have no actual experience with either.
If the truck is bouncing up and down and you determine yoou need shocks, I would look at either Bilsteins or Rancho's. I went with the Bilsteins, they did help the truck handle better but do not noticeable help with sway. The Ranchos have a huge following but cost more, both are very good.
I have Firestone Airbags with individual control, they came on my 2010 that I bought preowned. they DO NOT help stop sway, they DO level the truck. If I was doing it from scratch, I would go Stable Loads, have heard so many good things, great company.
If these things do not help- one ton dually, wish I went that way when purchasing my truck.