Hi,
I'm a local, and I've travelled all around my country.
Forget trains, argentinian rail system is from quite bad to incredible bad
Buses and planes are the way to travel to cover such long distances.
if you are on a budget, use buses. Overnight buses will be the best option to travel sleeping and don't feel the long hours (and save that hotel/hostel night).
Here, most you pay, better service you get, I mean, if you can afford the best service, do it! it will be a lot cheaper than flying yet. But if you cannot afford it, anyway you'll travel fine, just not luxuriuously.
yes, luxuriously
going to Iguazy, try to afford it and try the "Tutto letto" service by Via Bariloche bus company. The seat gets completely flat. The second best service (same car) is "ejecutivo", is still amazing. Believe me or not, at night, last hour, the steward goes offering a glass of whisky or champagne. I travelled a little abroad, and I know this service in my own country can't be beat easily.
Usually people spend 2 days in Iguazu, one day for each side, and please, visit brazilian and argentinian side, different experiences. But in fact, if you can devote one more day, better. There are other places to visit, and if not, the falls deserve to be visited more than once
I've been in Iguazu 3 times in my life, and I'll go back again, maybe this year, to take the Full Moon tour, which is expensive, but a friend of mine took it and got mesmerized by the white rainbows under moon light (only possible full moon nights, no rain)
which parts of patagonia have you in mind? it's very big, what do you prefer? mountains, woods and lakes, glacier area, coast? wildlife?