Although "that tactical vest might be the most appropriate", it might not. It doesn't really make sense to follow it with "but" anything.
The confusion between "its" (the possessive pronoun) and "it's" (the contraction of "it is" or "it has") is pretty common. The thing to remember is that other possessive pronouns (yours, hers, ours, theirs) have no apostrophe of possession, just like "its".