I can additionally recommend the GBA as an interesting fixed target. Lots of folks recommend an Arduino for this, and those are great little machines, but they have two problems. 1. they can be a bit
too limited for a lot of potential projects, and 2. because they are hardware projects boards, they don't do very much on their own. Figuring out what to hook them up to is half of the fun, but it can be a daunting choice for a beginner, especially someone learning assembly language for the first time.
The Gameboy Advance is a marvelous little platform. It runs a modified ARM7, so if you learn its machine language a lot of that knowledge will transfer into the industry. It runs at a brisk 16 MHz, which is fast enough that it can run compiled C code quite comfortably, but slow enough that performance still matters very much once you try to push the system's limits. Even if you run it in C rather than assembly (perhaps ideal for a true beginner), the whole machine is chok full of bare-metal standbys. Most of the graphics and sound hardware is memory mapped, requiring very specific bit patterns written to special addresses to tell the rest of the hardware what to do. Working with graphics requires an understanding of interrupts and synchronization. Finally, being a games system with a screen, buttons, and a speaker built in, there's a lot of projects you could build... but the easiest is to make a game! And what a blast that system is to make games for. Powerful enough to do all sorts of compelling things, but simple enough to program (even as a beginner) that you can easily have backgrounds and sprites onscreen in about a day of effort.