When do you use alternate picking? Is it just when you want to use it? Should I make alternate picking my primary type of picking rather than a continuous down stroke?
depends on what music you play.

But you should be able to use both (although it's fair to say that it's not required to be able to downpick as fast as you can alternate pick)
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Except children.
Yes, your will be better off, picking everything alternate. It'll be a tough habit to break, down picking, but alternate picking will help you with speed, precision, and loads of other techniques down the road.
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Most definitely. If you ever want to get faster you're gonna need to alternate pick eventually.

All down strokes give you a different sound, but the majority of your practice should probably be alternate picking.
if you are playing fast or slow its better and its more accurate
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Alternate picking is a must. If you just use continuous down strokes, you will get tired out very quickly and you will become more tense, making you play more sloppily.
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Junior's usually at least a little terse, but he knows his stuff. I've always read his posts in a grouchy grandfather voice, a grouchy grandfather with a huge stiffy for alternate picking.
Besides that, he's right this time. As usual.
You should use both.......they both have their proper place.
I find myself switching between both depending on what I'm playing at the moment. It should get to the point where you don't even think about it.........you just naturally use the one you need at the time.