Definitely use the Mopar or Fleetguard (same thing) filters on your Cummins. Oil filters are the wrong place to cheap out and Fram filters have been proven to be the worst there is. Cummins even said not to use them as they can come apart if wet and clog the system. NO Fram. Do some research.
Second thing is no K and N air filters. These do not stop fine dust and cause more engine wear that the stock filters. There has been a lot of discussion about this over the years. Again, do some research. The stock filters flow plenty of air and work well. One cool trick is to put the 6.7 air filter in the 5.9 trucks as they fit but have more surface area. The Mopar filters are very good.
Maybe the best place to get filters is from Genos Garage. Slightly higher price, but they have everything.
You can also get a magnetic oil drain plug from Genos that is a nice addition to the Cummins.
Synthetic oil is better, but better enough to make it worthwhile? I don't know. I have always run Delo 400 in my three Cummins for about 500,000 miles. I always change the oil at 10,000 mile intervals, except for the first one at 5,000 miles during break-in. None of them have ever used a quart of oil between their oil changes in 10,000 miles! They are great engines. But, I refuse cheap out on filters. That would be ridiculous. Use what Cummins recommends.
If your engine begins to hunt at idle, add a bottle of Power Service when you re-fuel. This will clear it up for a number of tank fulls and only needs to be done occasionally.
At about 100,000 miles the AAM rear differentials begin to chatter. These are in every truck starting with model year 2003. The limited slip will begin to chatter as you start out with the front wheel turned, as in making a left turn from a light for instance, or while maneuvering a trailer. It's annoying, but won't hurt the truck. The fix is to change from the stock 85 weight oil to 140 weight oil. Full synthetic. This fixes it.
Fuel filters can be let go for much longer than the factory recommendation. The change interval is just an estimate and has little to do with reality. If you get a bad load of fuel, a brand new filter could be clogged in a mile or less, and if you never get a bad load, the filters could go 50,000 miles with no trouble. So, you never really know. I tend to change mine at about 50,000 miles and I have never seen one dirty, except for once when one clogged that had a lot less miles on it and I suspected a bad load of fuel. But it's good idea to manually drain the water separator once in a while just to check it. Especially in the winter.
It's also a good idea to put a cap in the "capless" fuel filler. What a terrible design that thing is! It invites water and dust to enter the tank. A simple 1 1/2" expandable plumbing plug from Home Depot does the trick. But they are not fuel proof. So you can order fuel resistant ones on-line or from a plumbing supply that will last a lifetime and are cheap., Or, you can look at Genos Garage for their aftermarket ones that are fancy and expensive. Either way, cap that filler! Even the stock shipping plastic plug is better than nothing.