The system varies by river. The Rogue has a system, the Deschutes has a system, and the John Day has a system. There is a a ranger station on the Rogue most people utilize, and on the Deshutes there are businesses that are authorized to issue you the permits. The Deschutes is per person, and the cost is subject to what day of the week and what season you are paddling in. You can buy your Deschutes permit online, I do it both ways.
I prefer to purchase in Maupin. In 2013 I tried my best to arrange all of the little details, so I bought my permit the day before, for a total of 4 of us. The morning of the trip, my kids sister really wanted to join us, and so I said yes. Then I forgot that I needed get her a permit too, and it turned into a big hassle. Now I stop at the store when I get there and everybody is accounted for.
For rafts, the Sandy dries up pretty quick in the spring and summer. The Clackamas is runnable all summer, but gets pretty low for rafts. The Santiam is dam controlled, and they will not the cfs fall below a certain threshold (around 800 cfs at the Niagra gauge) to help the salmon out. We spend the majority of our late summer on the Santiam anywhere from Packsaddle park to Mehama. I don't do the Mckenzie a whole lot (didn't make it out there in 2014 at all) but it is really pretty around Paradise and Olallie. We camped at Olallie labor day 2013 and had a blast. There are great hikes, the Belknap hot springs, and other fun stuff to do there.
Wishing I was on the river instead of surfing the web...