I believe #1 is right in both circumstances. The exclamation point in the first one eliminates the need for the comma. In the second one, 2 is also technically correct, but there's nothing wrong with #1, it feels more natural, and also, since "That's the spirit" is a cliche, it probably makes more sense for it to be abbreviated anyways.
A grammar teacher would probably disagree with me, but as long as you have a complete sentence, I don't think using "or, and, but" is much of a problem in and of itself. The problem with sentences that begin with those words is that they are almost never complete sentences. So if you have all the parts of a sentence, you should be okay.
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