My ideal phone would be iPhone 5 form factor with an e-ink display running FreeBSD with nothing but calling, SMS, a text based browser, and a terminal. Minimize absolutely everything and jam a 6000maH battery in there.
As for "your ideal phone" - something similar might just be my next year's project, though sourcing the parts will be hard, for sure =)
Burner phones should be cheap and off the shelf. You can use a custom rom, with an open radio. If Qualcomm, QXDM/QPST to modify radio rom settings including modifying ESN/MEID/IMEI/Bluetooth Serial, etc.
You pick a off the shelf model that's easy to unlock, and flash.
You customize your own rom, and flash it. You eliminate all possible vectors of "hacks" e.g. oem apps and downloaded APK'.
Then the telecom service itself is where it'd e most vulnerable, in fingerprinting your geophysical location and such.
You can modify the GPS, to throw it off, sure. That's already done with rooted devices and you can eve thrown in a few mile obscurity, but, the tower location will ultimately pinpoint you through triangulation.
And keep in mind that there's also the fact that you have to buy the phones somewhere - that can be tracked, whether it's a package from eBay with 10 similar phones or just a guy buying the cheapest prepaid phones in a supermarket.