Unless you're one of those people that hates the way the default membership is implemented, or you have very specific needs for a membership provider, then there is no reason to avoid using the default provider. In other words, if you really don't care how it works, just use the default.
In particular, though.. MVC 4 uses the Simple Membership Provider by default, which is different from the SqlMembershipProvider (usually considered the default in most tutorials you'll read). You'll want to read up on how the Simple Membership Provider in MVC4 works.