Vancouver - Peru which bike?
There are a lot of good options and as many arguments for and against each. How much motorbike experience do you and your friend have? If you are both new riders, then smaller bikes could be a benefit. However, better to get some experience before the trip and then choose the right bike for the long haul rather then the right bike for your learning days.
As you don't want to spend much money, a used bike of some description is likely your best option, or a new smaller 250 cc or similar. In Vancouver, KLR's are in good supply - many at good prices and with low mileage. The older version is a bit more klunky then the new, but has a large tank stock, and tons of after market support for bags, racks, and gear. The Suzuki SE650 is another excellent choice available locally used - I don't see as many around, but those I have talked to really like them.
Fuel economy is another big factor as gas will be one of your largest fixed costs. Your can camp for free in the bush and eat day old tacos for months on end, but your bike will require a certain amount of fuel to make the trip.
I'd strongly consider a 250cc dirt bike, particularly if you can be disciplined enough to pack very light. These might be easier to sell or ditch in South America, although you need to look into this ahead of time - many countries require a bond 'Carnet' be posted specifically so you don't do this!
Be aware that any bike you buy will need some work and likely some modifications if you expect it to carry you the distance trouble free - make sure your budget allows for this. Buying a used bike with the right modifications already done is a good way to economize.
Do lots of research, attend a Horizon's Meeting, and read this site thoroughly.