I have been told that if you join a Signal Regiment and become fully qualified in your trade, you will have a greater-than-average chance/opportunity to serve overseas (as a reservist).
This is apparently because almost every deployment requires signals people, so that the troops can talk to eachother, and of course, talk to whoever runs the show from Canada.
That said, most - if not all - infantry units, and many armoured and engineer units, will have a plethora of ‘old dogs‘ who have served overseas, sometimes several tours. The 48th Highlanders, my unit, has a couple people with chests full of medals/ribbons that would put most US generals to shame.
But I don‘t think it‘s all about the medals -- I think it‘s all about the experience you get in doing something like overseas service. I‘d love to say more, but as I‘m Normy Newguy, I can‘t speak from experience myself.
If you really, really want to go over the water, I‘d suggest reg force. They do it all the time as it‘s their full time job.