Here is how I play the rhythm part of LaGrange. Our other guitarist does the lead, so I've never bothered to learn it (and therefore haven't included it :-)
Picking style is key to the percussive sound of this piece. Under each section I have placed the following symbols:
^ indicates picking with an upward motion v indicates picking with a downward motion
With a little practice, you can get a smooth up/down pattern esatblished, and it stays the same throughout the song.
E|-------5---5---5-----5---5---5-----5---5---5----------------| B|------------------------------------------------------------| G|.--------------------------------------------------------2-.| D|.--4/5---5---5---3/4---4---4---2/3---3---3---------------2-.| A|-----------------------------------------------0--0--3h4----| E|------------------------------------------------------------| (I usually play the D string with my pick and the E string with my middle finger. You can, of course, play both with your pick)
Repeat the break between |: and :| twice, then go back to the clean part (same as the very first section). Play it 4 times, hit the distortion, and play the same as the first verse until the fade...