I got a 1998 Gibson Le Paul a bit ago and have all of the setup done except for action and intonation. The guitar came to me with the strings at the 1st fret so low that I couldn't see any movement when tapping the string in the 1st fret with my left hand while fretting the 3rd fret with my right hand for any of the strings. This is very low. For me, if there is no noticeable movement on the high E string then I'm ok with that. All of the other strings need to be increasingly higher B-G-D-A-E off the 1st fret. I check all of this by eye and address the nut as needed. This guitar nut needs to be addressed.
A low cut nut leads to "ramp up" which to me feels wrong as in the lower frets I have low action but as I go higher up the neck the action gets higher and higher and higher. The top neck in the image below shows the ramp up.
The nut can change this. The 2nd neck in the image below is exaggerated, but the point is that raising the string at the nut reduces that ramp effect. This way after some tweaking I can get the neck to feel like the string is at the same height all the way down. I've raised the high E nut cut already and the ramp effect is gone for that string.
The second neck also shows where to check your action. With no frets pressed look at/measure the distance between the bottom of the string and the top of the 12th fret. The difference between them is your action. Action can change by cutting the nut slot deeper or making it more shallow, by changing the height of the bridge or cutting its saddles deeper, by changing your string gauge (affects relief--see below), and by adjusting your neck relief. People typically have a lower action for their high E string and a higher action for their low E strings. This is usefull because the heavier strings need more room to vibrate than the thinner strings.
The circle on the 3nd neck is where you check neck relief. Relief is the compromise between the stiffness of your neck and the pull of the strings against the stiffness of the neck. If you change your string gauge to a higher or lower tension, the amount of tension against the neck will change and you will likely need an adjustment to the neck's relief to get your action back to what it was before the change.
To determine your neck's relief, on the low E string hold down the 1st fret with your left hand and the body fret (press on 17 but 16 is the body fret) with your right hand. Then look at fret 8 and see the gap between the bottom of the string and the fret. The larger the gap, the more relief your neck has and you probably have higher action. The smaller the gap, the less relief your neck has and you probably have lower action. When someone says that they have zero neck relief they mean that there is no visible gap between the string and the 8th fret.