Sounds like you are researching all the bike options and will soon know more than most on that subject. I spent nearly a year in SA on my BMW R1200GSA (trip report here if interested). In the FWIW category, here are my thoughts on your proposed trip in general:

1. Ignore prior posts regarding people not liking people from where-ever. We (wife and I, from USA and on two bikes) rode with people from all over the world, including Australia, and never saw or heard of such. People everywhere were welcoming and friendly.

2. My guess is that for 4 weeks, renting is going to be your best option, curious what you find and finally decide upon. Someone mentioned inability to cross borders in that case - not sure about that, that does limit you somewhat, but see #3. Regarding the "buy" option; from what we saw second hand, is doable but can be dicey. Be careful and do your homework on that one.

3. But regarding borders: From my experience, I'd advise (as others) to concentrate on one country for four weeks. You can easily spend four weeks in Colombia (despite other comments - we spent over a month there and loved it), Ecuador, Bolivia, Peru, Chile, Argentina ... take your pick. If it were me, going back for four weeks after having done the longer trip, I would choose either Peru, for the Andes (NOT the coast!) and some amazing roads and sites, or Chile, where I'd start in Santiago and ride south and ride the Caratera Austral (Rt 17) all the way to Via O'Higgins. It is a bit of an out and back, especially from Puerto Montt to Villa O'Higgins, but between Santiago and Puerto Mont you can take different routes there and back. That's about 3,000 miles total, and one could start further south - there are rental companies operating in or near Puerto Montt and cut that mileage in half.

4. Timing: Peru is close enough to the equator that it is a mostly a matter of wet and dry seasons - we were there from late August into October and it was pretty dry and wonderful. The perfect time for the Carretera Austral is Dec-Jan - early summer. The wildflowers are in full bloom. Wikipedia articles are pretty good about having a climatology section with average temperatures and rainfall by month - I used that, in addition to reading other trip reports, when planning our trip.

5. Which bike. I think you know this, but it depends on you and what you want. I was on a big BMW R1200GSA and the big beemers are pretty ubiquitous in southern Chile and Argentina, in particular, and the BMW F700/800 and R1200's seem to be the most common rentals. But if you are wanting to do hardcore off-road, then a smaller bike would be better; we became good friends with a couple of guys from Canada who were spending as much time off-road on the trip as possible, and they were happy on their DR-650's. KLR's were also prevalent. We road dirt when we had to, and we had to often enough, but we didn't seek it out. And we saw people doing the trip on Harley Davidsons and one couple from Argentina on a Chinese-brand cruiser.

Hope that is of some help - and just do it! You will be so glad you did.

Jim