We went to Chile, Peru, Argentina and Bolivia in 2006.
We did lots of bushwalking and no climbing. Having said that there was climbing around in some of the areas siuch as in Patagonia (Chilean) and in Peru. The Patagonian climbing looked great. Obviously mountaineering in these places too.
I think you said something about bushwallking - it was great in all these places. Awesome. Chile was particularly good in terms of varied landscape - think glaciers down south with untouched bush and mountains in the background and in the north high altitude deserts with snow-covered volcanos as a backdrop. The middle has more volcanos but bamboo forests and lakes.
Chile and Argentina were easy to get around and safe (fairly good economies with all that brings in terms of fairly reliable and clean buses etc). Peru and Bolivia were a bit more dodgy but okay if you show a bit of good sense. Less reliable for travel. The people were all pretty friendly.
Not sure if your "up in the air" stuff is just finances or not sure about the destinations. Chile was easy to get around and would not be a big shock to the system if you have not travelled much. The downside (if it is your finances) is that it costs more than your listed destinations. It is not too bad but the accomodation options in some places, such as Patagonia are limited (but you can camp which is cheaper though only right next to fairly pricey backpacker and even better and pricier accomodation with beer and food for you to stare at).
Lastly, Qantas used to allow you to fly to Chile on a round the world trip and include the sector flights down to town closest to Patagonia. I assume they still do.