What maintenance should come first on a newly bought 5.9 Cummins?

First, identify exactly which 5.9 you bought. A 12-valve truck, an earlier electronically controlled 24-valve truck, and a later common-rail truck do not share one universal service checklist. If the engine has been swapped, the truck's model year is only part of the answer. Next, have the whole truck inspected. Brakes, tires, steering, leaks, cooling-system condition, and damaged wiring can deserve attention before any engine upgrade. Ask the shop to divide its findings into immediate repairs, scheduled service, and items to monitor. That makes the estimate easier to act on. Match the available records to the correct owner's manual and diesel supplement. Establish the oil and fuel-filter history, then review coolant, transmission, axle, and transfer-case service as applicable. Have the shop verify the valve-lash inspection requirement for your engine instead of borrowing an interval from a different Cummins application. Unknown history does not automatically justify a complete fuel-system replacement or a transmission flush. Diagnose symptoms and follow the appropriate service procedure. Record dates, mileage, fluid specifications, and part numbers for the work that is actually done. Spend the first few weeks learning the truck's normal behavior. A documented baseline and an unspent repair reserve are a better starting point than a pile of performance parts.