Do you need real-time-stuff - or do you need a OS that puts all request in a cue?
DSP (at least any feedback control loop) is often totally impossible to run in OS like Windows.
XMOS can make such things very easy since you do not typically use interrupts and have deterministic timing
Something that is like a small PC computer? well ARM is used everywhere in cellphones, pads/net-books.
Do you need both - there is TI's OMAP, with an ARM + DSP + 2 help units to control the communication between. There is both floating-point versions like the
http://www.hawkboard.org/ and other with a very fast ARM
http://www.pandaboard.org/.
You will heavily rely of the status of the last OS release with the open source stuff. Beagle-board has been around for a while, so maybe it is stable and reliable now.
Typically it's only when you pay 10X and get it from TI that you get the compilers to directly program the DSP's. But some OMAPs are com. with a low prices JTAG and a free version of TI code-composer.
If you want to program the DSP part, you will probably need an JTAG.
Myself I have many different boards from Arduino to a floating point OMAP with the TI code-composer.
But I really do not like interrupt-vector programming, so XMOS is the thing I'm always falling back to.
Consider to go for the
XC-2 with Ethernet if you go for XMOS. Then you have a fast way of com. to a PC-host independent of the OS or architecture. There is Ethernet sockets in almost all program languages.
With the XC-1 you are stuck with 1Mbit UART to the host, that enumerates as a virtual COM port.
I believe you have the COM port as well via the XTAG1 with the XC-2.
If you want to learn, XMOS is great since you have control down to the instruction level.
You can see each instruction in the disassembler that the compiler made, and XDE also interprets the meaning of it as ASM code.
Creating an OS from scratch to an ARM, ihhhhhh.
Only writing the memory page-swapping is a pain. I once took a University course in OS/distributed OS.
PS. Need a HDMI out? There is IC that has a 24-bit parallel in-> HDMI out for a few $. You can connect the MSB from XMOSport to each colour, and you have a colour HDMI out. (Colour 8-bit VGA can be done with some passive resistors only) DS.