Cost is never a problem. Many enthusiasts will be willing to pay moderate price for easily hackable high end devices. The problem is that ARM is a closed platform. There typically is a part named private ROM on the very silicon of SoC (system on chip). It blocks the reuse.
This part of ROM is responsible for picking a bootloader in some order: Z-Modem on serial, external Nand, serial ROM, SDCard, external USB. For every device the order is individual and poorly documented, you typically should hold few buttons when powering to branch into alternative loader. The image of bootloader if most of the time checked for digital signature of platform owner. So no luck.
For one off project it is OK to pick random device. But you possibly will be more interested in well known device, with published schematics and available source code for Linux, Android etc.
So my suggestion is to look at devices surrounded by active user's communities: Raspberry Pi, BeagleBone, BeagleBoard, some Samsung evaluation platform (PandaBoard ?)
My personal experience with TI AM35XX ended with disappointment with complexity of everything. The smallest Linux in the world named Angstrom has 3GB distribution image. The docs for chips are 4000-5000 pages. It did not feel much like a hobby and was not enjoyable.
The situation may change after Intel Atom SoC will become popular. I expect massive user interest and will follow the crowd in direction of smallest possible Atom with screen. Hope someone will complete a panel mountable piece with size of credit card and GPIO. It will be fun.