The main difference between using which and that is the difference between non-restrictive and restrictive clauses. A non-restrictive clause adds information to the sentence to clarify what it follows, but isn't required for understanding the sentence. A restrictive clause, by contrast, narrows the subset of items that the noun refers to, and as such, is necessary for full understanding of the sentence.
In your examples, you are referring to specific items -- there is only one hot dog made by you, only one DVD lost by you -- so you want to use that in these cases.
This is the hot dog that I made (as opposed to all of the other hot dogs here).
I'm finding the DVD that I lost (because I know where all my other ones are).
On the other hand, these examples are non-restrictive; they add clarifying information that can safely be removed without changing the meaning of the sentence.
These hot dogs, which I made, are excellent. (The hot dogs are excellent; that I made them is tangential to that.)
This DVD, which I lost, is my favorite one. (The fact that I lost it isn't necessary to understand that it's my favorite.)
Notice that "which" clauses are set off by commas, while "that" clauses aren't.