From the link, impulse as in "had an impulse" seems to both fit the context and correspond to the Greek. Is this simply a set phrase with no relation to other uses of εχω plus a noun? Is it equivalent to the constructions in English such as had a look/think/try etc ?
The reason I avoided "had an impulse" is that he seems to have already had the impulse. He has already been thinking about a Persian expedition and mulling it over.
ὁρμάω means "to set in motion," "to start up." Maybe "he got started" would do here. http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Do(rma%2Fw
ἔχω is used loosely in a wide variety of ways in idiomatic Greek. It's an all-purpose verb.http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3De)%2Fxw1
This is one instance where you have to get the meaning from the context, not the dictionary. Maybe "he got a start" would be English enough. But if you're reading Greek, you don't need to formulate an exact translation, as long as you get a pretty good idea what the author is trying to say, based on an understanding of the basic
meaning of the words and the context. That way you will be able to read more fluently and naturally.
πρὸς μέρος -- the dictionary is really owly a guide as to the range of possible meanings a word can have. "To this purpose" might do here for a translation.
προέθετο πολεμεῖν -- How about "he set a war as his goal"?