Just yesterday, one of my tuning pegs cracked. The more I turned it down, the lower the pitch in the string. if I tried to tune it up, it'd just stay at the current pitch. I later researched it, and realized that there's a simple procedure to fix it. I'll hopefully be going to a guitar store tomorrow to pick up a new peg.

The first question I have is, how often should this happen? Is it common, or is my guitar just a piece of crap?

It's a Lyon Washburn dreadnaught cut-away acoustic/electric guitar. Apparently the tuners are made of chrome.

Second, Should I look for a particular type of tuner peg tomorrow? Like, one made of a particular metal?
Zorbozate has the ideal answer for this kind of situation, they'll be able to tell you what it will cost to fix what and what needs to be replaced. However, if you posted pics of the damages, it'd be a lot easier to tell what is wrong.
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You win this thread. Pipe organs FTW.

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Let's take it one step further and add a slogan:

Big Bach is listening you!

That's the exact model I have. and I figured out how it cracked. Over time, the screw at the end of the 'handle' comes loose, and as I turn the handle, it puts a lot of pressure on the handle itself, rather than having a secured shaft. This eventually led to the snapping of the handle. I already know how to put one in. It's almost self-explanatory.