If you're going to rent a phone for the trip, then it's probably going to be a function of what is available.
One question you need to address is how often do you plan on calling? If you're only going to use this for an emergency, then you may not need spare batteries. On the other hand, most of these phones draw a fair amount of current, and don't last that long, particularly if you're going to be gone for more than a week.
You could carry spare batteries, or a solar charger, which can be very light, just a few ounces. I like the solar charger option.
I have an Iridum phone, and it works reasonably well, lighter would be nicer, but it's a good option. You can call for help, early pickup, or just status or say hi. You can accept incoming phone calls without burning the batteries by setting a predetermined time to turn it on for say 10 minutes.
One nice thing about all of the LEO, Low Earth Orbit satellite systems is that in a deep canyon or other obstructed area, you can typically at least get a quick call out, where with the Geosynchronous satellites, you can be out of luck.
Per the comment about using a PLB /EPIRB, these also work well in a real emergency, and typically are lighter than sat phones. There is no middle ground activating one of these beacons: If you really need it, then activate it. If you're anything from homesick or want a different pickup, it is of no use to you. The beacons only send a message of where your at and that you need immediate help.
One other note: You need to get the direct phone number for the local rescue / fire /ems / police for the particular area(s) that you would be in, as 911 from a satellite phone may not get you who you think you're going to call (or anywhere at all). If you call 911 and asking them what their direct dial number will probally only yield a 'what?' / 'just dial 911' response. In most places, there is a non-emergency number that is a direct dial number that gets you to the same call center.
Hope that helps,