Sorry about the late reply, been busy.
I would start from the very beginning before i suggest anything: what do you want to see? Culture, party, city, mountain, beach, etc? Time? Money?
Peru, for me, is a must. I love their people, their culture and especially their food. Out of this world stuff. I don't know (havent been in those shoes) but i would guess most of the places you'd visit are touristic enough, so I suppose you will be able to get away with English. Tone the accent down a bit, if possible. Nothing wrong with it but most people in latin america are used to american accents and strong accents (scottish, irish, etc) might perplex a few. Speak slowly, modulate and use your hands (not kidding). You should be fine. Be careful, try to use a call taxi, dont call attention, the usual.
I guess a few days in Rio are a must. The place is stunning. Just wander around, the location does the trick imo. If you are looking for beaches brazil is probably the place. Maybe north colombia.
I love Uruguay and would be my go-to place, but not for exploring which is what i guess you want to do. Might be a bit too quiet and cold depending on the time. I love it but i know the place, etc.
Chile is a bit like Arg in the sense that is long, has both coast and mountain, etc, so i would pick one.
Havent been to Ecuador i'm afraid.
Colombia i liked, but i was there with friends. Was more about the people than the place for me at the time. Didnt like Bogota much, loved Medellin.
Havent been to Venezuela.
Skip Paraguay for now.
I'll talk about Arg and i will make a few very hasty generalizations. Imagine Argentina as a right triangle.
View attachment 10992
Buenos Aires is the red dot. Right Side is mostly coastline (rivers to the north, ocean south from the red dot), left side mountains. Day/weekend trip to Uruguay from there, maybe.
North East: Humid and hot. Jungle. Iguazu Falls is probalbly the highlight of the region. Pantanal too: huge tropical wetland. if you are into animals and shite, go there. I would skip it unless i had tons of time/money.
North West: Hot but dry during day, cold at night. Depends how close to the mountains/high you get. Most underrated part imo. Beautiful, rustic, down-to-earth and cheap. Tucuman, Jujuy and Salta provinces. Amazing landscapes, decent wine, good culture/entertainment combination. Visit places during the day. Quite common for people to gather drink wine, eat local dishes and play traditional music (they are called peñas).
When i say amazing landscapes i mean that literally.
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You can cross to Bolivia from there if you are interested.
West (from red dot): main wine region (Mendoza). Tons of vineyards surrounded by mountains and valleys. Amazing and quite fun. Wine tastings and eating all day.
South (patagonia): HUGE place, i mean, like huge by south american standards, not Euro ones. You can see whales on the sea, pristine lakes on the mountainside, outstanding food. Expensive (by argentine standards) and again, everything is far apart. I'd pick one or maybe two places here. If you like hiking quite a few good spots here.
Nota bene: if you go to Arg, a few things you should be aware of. Might sound silly but they are important. Argentina has basically two exchange rates (actually more but trying to keep it simple). Official and unofficial (or blue).
You generally get a lot more for your money (Euros i guess) if you change them there in the unofficial market. Most places will probably accept dollars, depending on the exchange rate you agree on. Pretty sure your credit/debit card would get converted at official exchange rate. If you can, bring us dollars rather than euros. I don't stay in hotels there but i am 99% sure you can ask the clerks where to change currency and they will point you in the right direction.
Good luck and enjoy.
There's a "train in clouds" that goes to Bolivia somewhere there as far as I know? 
