I have to agree with what everyone else is saying. While, in theory, everything you need is there, the beagle is not the best platform for doing things like this first time. I have a number of examples of how to bring up a number of small microcontrollers http://github.com/dwelch67 and there are sites like http://gandalf.arubi.uni-kl.de/avr_projects/arm_projects/ and others with even more examples.
I have a beagleboard, baremetal uart out code, but sounds like you have that (in yagbat, for lack of a better place (wasnt worth its own repo) I have a beagleboard directory).
The msp430 launchpad is under $5 and not a bad processor. Made by texas instruments (same folks that make the omap) so the manuals should have a similar feel.
There is of course the arduinos, but you want to go around the sandbox, which is not hard, see my examples.
To stay in the arm family there is the mbed (around $50+), (avoid the sandbox, easy to do) and a good one that you might like because it is barely a microcontroller with all the stuff it has in it is the stm32f4 discovery board from st, I have links in my example page. It is about $20, goes up to 168MHz, has a reduced floating point unit (rare for a microcontroller) separate instruction and data caches, lots of ram/rom compared to other microcontrollers, etc. All at that giveaway price of $20.
A lot of these microcontrolers are going to be thumb or thumb+thumb2. The cortex-m3 and 4 are armv7-m so support thumb plus the full thumb2. the cortex-m0 and -m1 are armv6 based so only support a little thumb2, not enough to bother. I have a thumb emulator that you can play with thumb with (no thumb2 support), as well. I think the cortex-A in the beagleboard, is armv7 based so it supports the same thumb+thumb2 that the cortex-m3 and -m4 support. The stm32f4 is -m4 based the mbed comes in two flavors one is -m3 and the new one -m0 based. A lot of the cortex-m based microcontrollers are -m3 based as it came out first the -m4 and -m0 are just gaining some traction. You can with thumb or thumb2 start to use a unified instruction set which is a blurring between arm and thumb(2) allowing one source to assemble to both arm instructions and thumb instructions (with some limitations of course). So you can either just write in thumb/thumb2 and take that knowledge directly to the cortex-A (with one bx instructions to switch modes from ARM to thumb) or take your thumb2 code or unified code directly to the cortex-A and assemble as arm.
The biggest thing here is not really the learning of assembly though the key is reading the manuals, the more manuals from more vendors, the better you understand how to find the info you need for this more complicated target. With my experience I had a hard time with portions of the omap manual as well. Most manuals have errors, or are incomplete, etc you have to learn to work/hack through that, and that just takes experience. With the omap you will likely need to dig through linux or uboot sources for that platform to supplement the manual. Since the beagle uses a bootloader, its good because some stuff is done for you, bad because you need to reverse engineer both the hardware and software to figure out where to place your interrupt vector table so that you can perform interrupt based solutions. I highly recommend starting with non-interrupt, polled, based then slowly transition the knowledge to interrupt. Trying to hit a home run every time at bat will fail. Take it one base hit at a time.
