I have an Epiphone Swingster, bought three months ago new. The overtones from below the harp (between the bridge and the tailpiece) are so loud, paricularly on the upper strings that they ruin any single string playing and are amplified by the pick ups causing loud atonal squeaks. The G and B strings also slip out of tune frequently.

SOURCE: strings are very far away from the last frets on the neck...

Sometimes the truss rod (nut you are referring to) will do the trick. The truss rod runs under the fingerboard and allows you to give the neck relief or tension. Some truss rods are dual action but I'm guessing yours is designed simply to give basic relief of the neck. I would make sure the truss rod is adjusted properly before sanding down the saddle. If you sight down the neck you should be able to see the relief in the neck - just use the string as your straight-edge. Most guitars need a slight amount of relief but higher-end guitars can be almost straight (better fretwork.) Once the neck has been adjusted correctly you can move forward with the setup.

Make sure the nut is also the proper height. If the nut is too low (1mm height between bottom of string and first fret) you should get it replaced by someone capable of doing such a thing. If the nut height is okay I would suggest moving forward cautiously by sanding the bottom of the saddle. Make sure this is done patiently and carefully as it can drastically change the sound and playability of the guitar. Hardly any material needs to be taken off to lower the action just a little. Error on the side of not-enough than too much. Make sure the bottom of the saddle remains flat! If the bottom isn't flat the guitar can sound horrible and if there is an undersaddle pickup it might not pick up evenly. The easiest way to do so is to tape some sandpaper rough side up on a flat surface (just don't pick something like mom's heirloom or something important in case it gets scratched.

If you'd like more detail check out http://www.fretnotguitarrepair.com/Repairs2.htm

Good Luck!

SOURCE: which string used for epiphone gibson lea paul special II guitar

This is really a personal choice as long as the strings are made for an electric guitar there are hundreds of different kinds, it mostly has to do with the thickness of the strings and how the thinner the string the easier it is to manulipulate, you should go to a good music store and tell them what type of music you play and they will give you some choices.