This question is bound to get a lot of discussion from each group of Suburban fans out there.
So I will start with my overly biased opinion just to make this easy
These are the basic things I would want.
1. 3/4 ton
2. Leaf spring suspension
3. Air bag over loads
4. Low gears 4.10 is a good all around ratio
5. Updated rear brakes.
6. Full floating axles
7. Manual transmission
8. Engine set up for low end torque
9. Heavy duty engine cooling system
10. Class 3 or 4 hitch, set up for torsion bar system.
There are many ways to achieve the above, it all just depends on the direction you want to take your Suburban build.
Stock?
Modernized?
Stock:
Personally I would just save all the hassle of a build up and just find yourself a K20 Suburban, since it will have all the beef in the chassis you will ever need right off the bat.
Modernized:
The sky is the limit, depending on your bank account. Lets just say you have no issue with funds, and are not in any kind of hurry. Start by finding the most solid and complete Suburban you can afford, doesn't matter what it was optioned with from the factory since you will replace it all anyway. The goal is to find one that has the best overall quality in the body work, and the complete interior in ready to live with condition.
Drive train.. You could find a rolled over new Chevy/GMC truck, buy it whole and then swap the drive train into the old Suburban. Or, you could just buy each piece new from GM or from a quality shop.
Suspension.. If you are not interested in 4x4, then you can put in a whole new air ride suspension. If you are interested in the 4x4 route, then it's a cheaper and easier route IMO.
The list of ideas and suggestions can go on and on, but first we need to know what your desired end result should be and what kind of money/time you are willing to spend.