Okay, so I am getting a new tube amp soon for my birthday. My MIA Strat runs through my Spider Line 6 III, which is awful, and on positions 1,3, and 5 there is a buzzing. If I get a tube amp, will I need shielding as well, or will having a higher quality amp reduce buzzing?
you should shield the guitar.

it'll be an improvement no matter the amp.

guitar nuts is a little detailed, you can get away with less.

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Set up Questions? ...Q & A Thread

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Most single coil pickups have a good bit of hum regardless of the amp. Shielding will help though.
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You will never get rid of the hum completely. In positions 2 and 4 the 2 single coils are out of phase and cancel the hum. High gain and high volume will make the hum of single coils worse. Shielding will help some.