Steves comments are spot on. Also, if you want to experience the culture, keep the distance down and explore the back roads. With the same goal in mind, start learning Spanish now, before you leave. The language learning process is an enriching component of the experience. Don't expect to be fluent.

A 250cc moto (and locally licensed) is definitely fine in Colombia, Ecuador, and Peru. You won't hesitate to go off the main roads. It's also a good choice if you want to go inland during the rainy season (mud, stream crossings, bumpy rocks). Inland is where the local culture lives. Many travelers on 600cc plus motos are reluctant to leave the main roads and miss so much. That's my observation.

I have a moto stored in Peru, and I've made 3 trips, each about 6 weeks, mostly in Peru, mostly during the rainy season. I still have more to see & experience. Go for quality travel, not distance. The mountains in South America are taller than anything in North America, and the ruins and ancient culture are rich and not to be missed.

Street food and posadas are so inexpensive that it's not worth bringing camping or cook gear. I've traveled on less than US $40/day for food, room, gas, repairs, & daily expenses. If you buy a locally licensed moto, you can store it in the country of origins without a TVIP. Foreign moto, you are limited to 3 or 6 months in most countries.

Buen viaje!!