On the other hand, my expenses will also be in US dollars. To what degree should I hedge against the dollar?
Ultimately the point of hedging is to diversify. So the degree you should hedge is relative to the degree with which you have exposure to your home currency. So for example, if you already own a home in that country + you already own lots of shares in that home currency, then hedging might be less important.
The recommendation I've seen is around 25% of your portfolio in hedged global equities, assuming you have another 25-30% in non-hedged global equities.
I'm actually not sure in your case. My guess is that it's something you wouldn't need to worry about, but I don't know.