Some interesting opinions posted over the last four pages but it seems to me those coming from the "why pick one style, learn both" school of thought are not really addressing Plastic's original question. Maybe both are important but I'm guessing as he/she is thinking of taking lessons finances may only permit learning one technique for now - thus the question. Which one first?

For me there is no question. All you have to ask is which came first Blues or Shred? I hope you all answered blues so the next question is what style did most shredders learn before they learnt to shred? I think the answer in most cases would be blues again.

Personally I hate shredding and can't see the point of it. I can listen to about 30 seconds of Satriani before i want to put my boot through the CD player. Wickipedia defines shredding as " a guitar playing style where technical proficiency is the major goal".I.E. technique above phrasing, melody, emotion or any of the other thing for which the Electric guitar is justifiably famous.
Can anybody put forward a convincing argument to me that ANY Satriani song is more beautiful the The Thrill Is Gone?