I just picked up an 89 Cherokee for 150$ Drives good, needs paint. It has two issues, needs an alternator and a spray pump for the windshield wipers.
The interior has zero stains, rips, or problems.

What are the common problems on Jeep Cherokees? Anything I should do right away? Takes a few cranks to fire up.

 

renix era jeeps start slow so no worries there
find cruiser54's tips and tricks and just do all of them. it will save you a headache

 

True about the cranking and all-around excellent advice.

I would recommend replacing all fluids and performing a tune-up (oil and filter, plug wires, plugs, air filter, cap and rotor). Check all vacuum lines and replace any that appear weathered or cracked. Check your injectors for signs of leaking around the joint where the metal barrel meets the plastic cap. They can be replaced with either 703 or 764 (Is that right Flintstone?) injectors from the junk yard. I would also replace the Crank Position Sensor (CPS) with one from the dealer or NAPA. They're sort of like timing belts, they fail after a period of time and if you don't know when it was last replaced, the chances it will leave you stranded somewhere are high. Fortunately, they can be replaced in an hour or so and require no mechanical knowledge and cost about $50-$60.

 

Yes, aside from F1Addict's advice.

Click on the link in my signature below and do 1,3 4, and 5 at a bare minimum. Costs about nothing except an hours time and addresses known issues that will haunt you at some point down the line.

 

I would also check, or have checked, the fluid levels and conditions in every gearbox, diff, power steering etc etc before driving it much.