Taking Vanguard for example, VGS is global equities, but VGAD is global equities that are AUD-hedged (my home country).
The only downside is that you pay more in fees (and they're less tax efficient). People generally don't bother with it though, because on a long enough time-line currencies usually revert to their long-term average, so if you're holding for retirement there's generally little point.
This is a _huge_ downside for index funds, though. Even quite a small fee difference has a huge compounding impact over time; people often miss just how much.
AIUI, assuming you're investing in a global equity fund, currency hedging is almost never worth it. It _may_ be worth it in some cases if you're investing in a foreign index (eg S&P for Europeans), but even then not usually.
Hedging is all about diversification at the end of the day. So it makes sense to hedge if you're coming close to retirement age.
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.