"Safety" is always first.
Brakes,
Suspension,
Steering
Lights and wipers.
Be aware that your vehicle probably has the "JN3" brakes; the crappiest brakes GM ever put on a GMT400 vehicle. Upgrading to a Treasure Yard JB5 or--even better--JB6 should be a high priority. There's no sense spending money to replace JN3 calipers or rotors when you could upgrade to the better stuff. Same with master cylinder and booster. And I've harped forever on the travesty GM dealt the 1500 trucks in the rear--the leading/trailing shoe brakes are a mess. You need different hubs to make the bigger front brakes work. I just grabbed the entire steering knuckle with control arms and shocks, with rotors and calipers from an "extended-cab" pickup. The master and booster, too. Then I can rebuild the control arms (ball joints, control arm bushings, check for bends/twists, etc.) before removing the original parts from the truck--less "down-time".
There's nothing inherently wrong with the suspension, although "my" '88 K1500 RCLB did not come with a front sway bar. Very recommended. Again, this is a simple Treasure-Yard pull; plus new bushings and end-links. If that truck has been carrying a snow plow--as indicated in your photo with the plow lights and hydaulic ram--expect the front suspension to totally wiped-out--ball joints, control arm bushings, shocks, tie-rod ends, etc. Could be the torsion bars are fatigued, too. Hard to tell.
The biggest single problem with GMT400 steering is the rag joint at the steering gear end of the steering shaft. I replaced mine with a "new" GM C3500(HD?) lower steering shaft that has a U-joint instead of the rag joint. HUGE improvement.
I upgraded my headlights by replacing the sealed-beams which still worked--but had corroded reflectors; and I added two relays to the circuit to improve voltage at the lights, making them brighter. Protect the relays and headlights with SELF RESETTING CIRCUIT BREAKERS, not fuses. (one 10-amp circuit breaker for low beam, one 15-amp circuit breaker for high beam.) Assure that the headlights are aimed properly.
Most of these mods are described in detail, with part numbers elsewhere on this site.
Then all fluids and filters. Where possible, inspect the parts you're draining fluids from--look for debris on the magnet in the rear differential, look for debris in the trans pan, etc. Otherwise, drain into a CLEAN drain pan, and look for chunks that settle-out.
You need to inspect EVERYTHING made of rubber-natural rubber or synthetic rubber: Belts, tires, hoses, suspension and chassis bushings; etc.
Of course, you need to identify other problem areas; when you're doing the brakes, you'll be looking at the rubber brake hoses. When you're flushing coolant, you'll be looking at the rubber belts and hoses.
From there, the usual "tune-up" services for the engine--cranking compression test, cap 'n' rotor, plug wires, spark plugs, verify PCV and EGR, verify base ignition timing and timing advance, etc.
Check fuel pressure. Connect a scan tool, look for "codes", but also look at the data stream. Verify all the sensors, assure that the IAC and EGR are working. (You can try to assess the condition of the O2 sensor; but you can pretty-much expect to replace it.)
