To clarify, there is only one UTM grid, but as mentioned GPS's can use different map datum. You'll want to set your GPS datum to match that shown on the map you're using.

When using paper maps I highly recommend looking at maptools.com. Their tools - or similar map grids from other sources - make quick work of translating locations from a GPS to the map - and vise versa. When doing this I find it much easier using UTM coordinates, though to be honest I constantly find myself having to relearn how to use the grids on the map (might be some neurons damaged from my youth).

I'm a big fan of folks learning to use a paper map (good water resistant topo with UTM coordinates - I purchase mytopo.com maps), a baseplate compass with adjustable declination (set to point to true north - my favorite is the Suunto M-3), and a mapping GPS (set to match the paper map datum and displaying UTM coordinates).

Regarding GPS durability, so far every single one of my GPS units are still functioning - even my very old Garmin GPS III Plus and my Garmin Gekos, though their interfaces are archaic compared to today's units. BTW, I never rely on the GPS unit's water resistance! If you're concerned about batteries failing - make sure you buy a GPS that can use lithium batteries (less tendency to leak, better performance in cold, lighter weight) and bring along plenty of extras (a pack of 8 costs about $20). Oh, and the #1 rule is to set waypoints to my truck and other nearby key locations that will help me get unlost.

When preparing for an outing I use this website to convert Google Maps lat/lon coordinates to UTM:

http://boulter.com/gps/

My favorite book on this topic was GPS Land Navigation by Ferguson & Tucker, but like me it is a bit aged by now. Still, the key points haven't changed. I like that it emphasizes use of paper maps and GPS units TOGETHER, and it stresses practicing in your neighborhood before going out to more remote locations. I haven't kept up on the latest books available.

BTW, when using my car GPS (Nuvi) I use dd.dddd format lat/long coordinates rather than UTM. Faster conversion from Google Maps.

I tend not to worry about what coordinate system rescue crews use versus what I use since I likely won't be communicating with them. My objective is to not be lost, and if lost I can use my tools to get myself unlost again rather easily. If necessary (life at risk) I can use my PLB to get help and they'll receive the coordinates from the PLB.