That is a tough question. I think Cummins is probably the best choice in a diesel motor in those years although the 7.3DI guys sure seem to love them. My big concern is that with the years you're looking at there is a risk of a serious failure. That's just the nature of the beast with a used vehicle.
So...despite your thread title I'm going to comment on the rest of the drivetrain and suspension. First and foremost, I would avoid the automatics in trucks of that vintage. Yes, they can be built up, but that's $$$. With the mileage you're going to be looking at it would be best just to budget for a new transmission if you decide to go automatic. The exception might be a GM truck with a 4L80E transmission. These are just the old 3 speed Turbo 400 with an external rearmounted overdrive, much the same as Dodge's 46RE is a Torqueflight 727 with an external overdrive, but GM's execution was far better and these have proven to be reliable transmissions. With the most powerful engine options only being the 6.5 turbodiesel or a 454 big block though it's easy to understand half of why they have proven to be reliable.
Ford and Dodge both used the same transfer cases in those years. I might be willing to argue that the NV271 and NV273 transfer cases are the most bulletproof light truck t-cases ever. They are rated to a higher GVWR than the old NP205's were even. An earlier Ford MIGHT have a Borg Warner case, but I don't think so. A Chevy is going to be an NV241HD I believe. It wasn't until 2001 or so that the NV261/NV263 became available AFAIK. The Chevy cases are lighter duty than the Ford and Dodge units in theory, but I haven't see failures so it must not be that big of a deal. Some GM stuff will have Borg Warner cases too if it was set up to run a PTO. No worries though, even though they aren't common they are strong.
In terms of rear axles it's a bit of a toss up. The Ford 10.5 inch "Sterling" rear is tough as nails. Dodge has always used overkill in the axle department so you're likely to get a Dana 70, Dana 70HD, or maybe even a Dana 80. You're not going to hurt them. What's scary is that the new 11.5 inch AAM axle Dodge us using is even bigger yet. A GM product is going to have the venerable 10.5 inch 14 bolt full floater assuming you are looking at an 8600 lbs GVWR truck, not a 7200 lbs GVWR truck (although the 7200 lbs trucks are a nice step between truck sizes).
On the front end you start to run into some differences. No matter what you're going to have unit bearings (hub assemblies) in those years. Ford is going to have either a Dana 50 or a Dana 60 depending on year and if it's a 3/4 or 1 ton. Neither is terrible though the Dana 50 is a bit of a bastard child. In either case you're going to have balljoints instead of kingpins like the old trucks. Also, the auto locking hubs on a Super Duty are a suckfest. At least that whole front end comes apart with a 21mm socket. A Dodge is going to have an AAM axle in those years to the best of my knowledge. They are a stout unit, as are the Dana 60's they use, but again, you have unit bearings and balljoints instead of the good stuff of yesteryear. You also will have drive flanges and a central axle disconnect instead of locking hubs. I prefer locking hubs, but Ford's automatic vacuum hubs are not what I'm talking about.
The GM stuff is the bastard child. Since the truck has IFS it's going to have a split case high pinion AAM front. The differentials don't seem to be a problem, but the axle seals will always leak even with the new seals from GM (on revision 20 or something to the design and they still don't work). The CV axles are tough as far as CV axles go, but the boots do tear and the joints do wear out. Still, I'm not sure they I find them any less reliable than the solid axles for general use than the solid axles on Ford or Dodge. They will run smoother on turns and the joints are easier to service. The killer on the GM stuff is the IFS. It wasn't until GM went to rack and pinion steering and coilovers on half tons recently that the suspension and steering problems seem to have been somewhat improved. Expect to replace balljoints frequently. Also, the tie rod ends, pitman arm, and idler arm on these trucks just flat out sucks and it will wear. Aligning them is also a lot harder than the solid axle rigs, but that's not really your concern.
If you had specific questions about anything else I'd be happy to help out as much as possible.