All you need to know about safety while traveling in South America is: Avoid to walk by yourself at night; never leave your place carring cameras, walet, bags if you're going to a party. Local buses are perfect to get robbed
( it happened to me many times in Brazil, 1 time in Argentina and Paraguai). Don't carry a lot of money and be aware of those people that loves tourists and wants to take all your money.
To travel by plane to all those countries you wanna go It's very expensive and by bus sucks cause the highways are horrible. You would spend more time inside the bus than enjoying the places you'll visit... By train... I've never heard about someone who traveled around South America by train... At least in Brazil this is impossible. So I'd recommend to buy plane tickets with stopover (I don't know if this sentence is correct but anyway I hope you understand me).
But if you're looking for a good time and adventure just go! South America has beautiful places, people and lots of culture to be learned. You won't regret! Have fun!