for buying a bike locally, I am currently looking into this as well. I am considering Bolivia (there is a thread here on this if you search) or Peru.
Toby can help if you buy in Peru:
Both countries seem th easiest to buy a bike.
For your timing, as you plan to ride to Ushuaia, remember that seasons are reversed. Getting to Ushuaia in the beginning of winter will be cold and possibly snowed in. Unless you get there in february/March and if you are lucky....
We rode to Ushuaia in Xmas/new year (dec 2007) and we still had a bit of snow, and that was mid-summer! it was extremely cold.
Also, if you plan to cross the salar de Uyuni, around Feb. to April it may still be flooded, so not possible to cross on a motorbike.
You could buy your bike in Chile too and ride south before going up north.
There are threads here describing the process of buying a bike in Chile.
I would advise you to learn as much spanish as you can before leaving. Lots of free stuff online. I used lots of online material for russian for example (for my last trip - and used my little russian a lot!)
It will come handy. Don't expect everyone to speak english. They don't!
3 months is a short time to do all of south (and central) America. It can be done but you will spend you life riding....
SA is a very big place! distances are huge.
Would be a shame to rush. Maybe buy a local bike and do by sections, storing your bike in between trips? Javier in Buenos Aires can store your bike. This is what I have in mind if we buy bikes in Peru/Bolivia. So that we can come back and keep riding....