Well, you are about to get a somewhat unobjective opinion here since I work for Small World Adventures, but here is a bit of a low down on the paddling in Ecuador.
Nov./Dec. are great months to paddle in Ecuador (really the prime season is Nov. through March). It's technically the "drier season" in the region where most of the good paddling is, which is good. Flooding rivers are much more of a problem than dry rivers. Having said that, it still can rain a lot during these months so come prepared for anything!
If you had to pick one kayak to bring to Ecuador, I'd say bring one of the cross over river runners/play boats. There is tons of good creeking in Ecuador (much of which can be done in a "tweener" boat), but there is also a great abundance of fun, big water play runs. So if you want to sample a little of everything a "do it all" boat is good. If steep creeking is your style, bring a creek boat as long as you won't mind missing out on the play runs (or, come on a trip with us and use a creek boat for the creek runs and switch to a play boat for the play runs
Now, I'm not just saying this becuase I'm biased, but if you only have 1 week, I'd seriously think about doing a guided trip. Mainly just because if you come with us on our weeklong trip, you'll get 7 great days of paddling, you get to stay at our awesome riverside lodge, have your choice of over 60 kayaks, and we take care of all the logistics. All you have to worry about is having fun paddling. In one or two weeks it really is tough to do it on your own and get in as much quality paddling.
If you have more time (3-4 weeks) doing it on your own can be fun too, as long as you speak some Spanish and can be patient with challenging logistics!
Either way, you should check out our guidebook. You can order it online at www.smallworldadventures.com
You can also check out our blog at www.smallworldadventures.blogspot.com
and look at some of the trip reports to get an idea of what sort paddling Ecuador has to offer (it has a great variety of Class II through Class V runs both low volume creeky and big volume, so really a little bit of everything).
Ecuador is really an awesome place to paddle, so I'm glad it's come under your rader--I'm sure you'll love it!
We do rent kayaks as well if you decide you do not want to bring your own.
Oh, and did I mention that we run kick ass kayaking trips (kayaks are provided on our trips)?
If you have any further questions, please feel free to e-mail me at email@example.com
Whether you go with us or on your own, have a great trip down there, hope to see you on the river, or at our lodge for a beer.