Included in the typical definition for a motive (or "motif") is that it is something that recurs with some frequency later in the composition (this includes the development of said motive).
In this sense, a chord progression could be considered a particular type of harmonic motive depending on how it returns throughout the piece. Typically, though, if the repetition of a chord progression is only due to the repetition of a section of the piece (e.g., the chorus of a rock song), we don't typically think of that as a motive, because the repetition is less about the chord progression and more about the formal unit. If, however, you're dealing with something like a chaconne, where the entire piece is constructed off of a repeating chord progression or bassline, then said progression can typically be considered a motive (though we usually use the term "ostinato," which just means "something that repeats").
Some composers, like Richard Wagner, have managed to create a motive out of a single harmony. In this spot in Die Walküre, for instance, Wagner uses a
Dm add6 (or
bø65) that returns in various guises to suggest "misfortune."
As for "Is it better to start off with a harmonic motif before a melodic one?", that's completely subjective, and different composers/theorists have different opinions.