In reply to neil9216:
Hi. I've only been to Ecuador, but from what I gather, the travel situation there is similar at least to the other Andean countries.
Public transport is generally excellent and cheap, as for actually carrying it, well you know how much you're able to carry better than anyone. I can see a couple of issues though.
On the buses, the driver will encourage, maybe force you to put your backpack on the roof. I never wanted to do this as as a westerner luggage goes missing from the top of buses with some regularity. The alternitive is to have it on your lap, which with a rack in there too could be bloody uncomfortable. Another option is to buy a big sack from a market once you're out there and always put your rucksack in it before putting it on top of the bus. That was everyone will just assume it's another bag full of dead chickens, or something.
There are usually ejecutivo (executive) buses, which cost a bit more, but are genrally much more secure. Prices will obviously add up over several thousand miles.
Likewise, I always felt most vulnerable to theft/mugging, when walking to and from bus stations with my bag on my back. The more mobile you are, the safer you are.
Lastly, if you don't have any gear, you can't really climb can you. Unless you're travelling with a climbing partner though, I guess you're relying on meeting other climbers? If so, you could gamble on them having gear and just take shoes and a harness.
The alpine gear I saw for hire out there was shoddy at best, not sure I'd trust to hire a rope, unless the outlet came with a sound recommendation.
Hope you have a great time either way!
Ceers,
Tom