its difficult for us to say much here and in the end you will know how to do a simple setup for the LP. You will need to hands on, adjust the thing and look out for the result, thru playing the instrument, listening to it yourself. And the thing is, the more you do it, the more you will know how the thing work.
Its directly opposite to reading on how to do it, coz the more you read(without working on it), you will be more confused(coz certain setup, can be explained differently, but meaning the same thing. Without hands on experience, you cant understand just by reading)
anyway, for what you have asked(do know that what you have asked, are enough for some to write an entire book on, so do pardon, if the following are just brief desceiption)
1) Adjustment of truss rod, from the way you are asking, it seem like you might still be a bit unsure on why the need to adjust truss rod. The things which you wrote, are the way to check the curvature of the neck(through truss rod adjusment) and neck relief(pressing of strings on 1st fret and 12 fret while checking on 6th fret). These 2 thingy are the aftermath of adjusting the truss rod.
2) Bridge adjustment- Bridde is where your strings sit on, theres 2 adjustment which can be made, one of it, is at each side of the bridge, which affect the height of the strings in relation to across the fretboard(In short, it affect action. guitar action is the gap from the top of your guitar fretwire to the bottom surface of the strings(higher action, you will have to press harder on the strings against the frets to play the instrument. Lower action, easy to play the instrument, but might result in fret buzzing)
The other adjustment in the saddle affect intonation.
3) Pickup height affect the magnetic pull on the strings and the volume. Pickup as the name inply, is a "pick up". Its made of magnetic with wires running round it. Our strings are made of metal, the vibration of the strings will cut the magneticfieldwhatsoever, convert mechanical energy to electrical energy and output to amp source. If pickup close to strings, volume of the instrument will be louder as well.
The adjusment of pickup height is to make sure that when you switch between different pickups and the combination of pickups(in LP only 3, bridge, bridge+neck, neck). The volume are more or less constant(or if according to individual preference, can be set unevenly, for rhythm playing and solo playing etc)
4) Tail piece adjustment- Affect the break angle of the strings, which in turn affect tension/sustain/blah blah blah. I am not to particular into this adjustment, so most of my guitar with stop tail, its all the way down. Perhaps others can add in for this or try searchng for more info on stop tail strings break angle.
5) Adjustment of the saddle(intonation) work hand in hand with the adjustment of the truss rod for neck relief.
Action- Distance/gap between the top surface of the fretwire to the bottom surface of the strings. As affected by guitar nuts, truss rod adjustment, bridge adjustment etc
The sequence, my preference only
1) Truss rod adjustment, if any. Once done, check the neck relief and making sure all the notes across the strings are even and not having any with the same note across 2 different frets
2) Tune up and check whether the bridge height is ok with me. If not, loosen strings, adjust bridge(if dont loosen the strings, the pressure from the tighten strings will force down on the bridge and making it difficult to adjust it)
3) Stop tail- i dont touch the stop tail usually(so usualy i leave it all the way down)
4) Stretch the new strings at least 3 times, across all 6 strings. After each stretching, i will retune all 6 strings, check for intonation and do any minor adjusment if need to.
5) Once strings settle, tuning done, intonation done, comfy with action, then i do the pickup adjusment. Polepiece, i dont touch not see the need to. I will just adjust the pickup height, with the side on the bass strigns(thicker strings) slightly lower and the side on the treble strings(thinner strings) slightly higher.
I will do the same for the other pickup. Once done, then i switch to the middle position to make sure that switching in between pickups, i wont have too big a volume different.
Anyway, above just a brief short words on my prefered way of doing things. So it might not apply to others, dont follow everything, just pick out the main point and verified against other sources for comparison. In guitar, theres often different way of doing same things, according to preferences of others. Dont get too occupied/rigid with preferenes of others.
have fun and more confusion i supposed.. haha
