I went through this same thing in Feb/March, - What I had to fix/change immediately after buying mine.
All this has been mentioned before and I used most of the information in this forum when I bought mine.
You can also google most of this stuff and watch videos or read about what to look for. Which helped me tremendously.
I took the LX, removed all the skids and engine plastic and drove to an independent dealer and had them do a "pre-purchase" inspection before I bought it.
It checked out fine and the mechanic actually missed a few things I listed below and they made up a few things too, but that is not what this is about. : )
-Check the engine for "oil seep". Remove skids - Usually on the drivers side, if you see it, you will know... If the seep is bad or the skids are covered in oil, walk away...
-The Radiator will need to be changed if it is OEM. It WILL have leaks at the top as already mentioned. ($400-$500 -can be done in your driveway with a buddy)
-The brakes are probably worn and maybe the rotors too. (full brake job in the driveway can be done)
-Check the headlight washers work and are not leaking or broken. (they only pop up when the heads lights are "ON" ...not the auto setting.) (Expensive repair)
-Check the head lights, all the bulbs - fog, low and high. Those things cab be expensive to replace if you go with the high end bulbs.
-Key Fob Batteries... mine were dead. If you have the credit card key fob... that's a plus. Those are cool.
-Check all 12v power outlets and USB connection - My fuses were blown and the previous owner I don't think knew they were blown. (fuse #26 under dash)
-Check the spare tire and the TPMS (look on the dash as you flip through the different vehicle displays)
-Check ALL the 4wd functions - on Grass of course... Listen and feel the vehicle when doing this. IF you think something does not feel or sound normal, ask on here.
-Check the AHC and play with it, go up and down, up and down... (doors have to be closed)
-IF you purchase, go ahead and get a new gas cap... LOL
-Check the battery - might be time for a new one - Mine died a week after I purchased.
-Wiper blades, if they have the OEM wipers installed, you can buy just the OEM strips, which will save a lot of money.
-Last Oil change?
-Transmission flush?
-Connect an OBD2/link/scanner and check for codes or any cleared codes. (you can get them on Amazon and they work well)
Mention this stuff to the seller and start making offers deducting the costs of replacing the radiator, brakes, etc etc... You know the drill. : )
Good luck, let us know what happens.