I too have read a lot about the 2015/16 CR-V vibration caused by the CVT that I wish they never put in. I doubt it'll be a reliability problem because it's only a vibration and Honda's CVTs have proved to be very reliable for the few years they've been selling them. If you keep your car for a long time, take the 2015. The 2017 has the new turbo in all trims but the LX (bottom of the line). Turbos need to bemeticulously maintained in order for them to last which is why I think you should stick to the 2015 all trims or 2017 LX trim. Of course the 2017 is more fresh and new while the 2015/16 is sort of outdated.
The Toyota RAV4 is even more reliable than the CR-V, but the CR-V is more comfortable.
I don't see how you can get a 2015/2016 CR-V for $15k, so if you can't get those years than look at a 2013 RAV4. I know someone who just bought a 2014 RAV4 and they like it. If it were my money between the 2015/16, the 2017 CR-V LX and the 2013 RAV4, I'd go for the 2017 CR-V LX and after that I'd take the 2013 RAV4 because at least you could get an upper trim RAV4 with more bells and whistles. There is a traditional 6 speed auto in the RAV4, better reliability, and no vibration.
As for the used cars being less reliable than the new ones, this isn't always true. Good reliability research is needed to be sure. Check this Consumer Reports and TrueDelta for reliability ratings. An example of automakers that have significantly dropped in terms of reliability include Acura, Subaru, and Honda (only a couple cars, not the CR-V). Older cars like a 2002 CR-V compared to a 2017 CR-V, the 2002 will obviously almost always be less reliable because of wear and tear.
For the warranties, don't buy them for reliable cars like the CR-V and RAV4. It's a huge waste of money. Save the extended warranties for the Germans, Chryslers, Fords, and GM cars.
I'm a Honda and Toyota fan, but over all of these cars, I'd take the 2017 Mazda CX-5 (just as reliable, if not more so than the Honda and Toyota), but that's just me. Test drive all of them to see which one fits best.