@vertigo @alcinnz @raccoonformality Seconded. The 6502 is a great choice for learning what programming in assembler is like, but pick hardware that has a frame buffer.
The BBC Micro is a pretty good choice because the assembler is available from inside BASIC (so you don't have to do literally everything in assembler to get started), and the hardware is a simple memory-mapped bitmap, rather than having things like sprite hardware or tiles to worry about.
Another option is BBC BASIC for SDL with built-in assembler support. You could run it on an ARM device like a Raspberry PI; ARM assembler is pretty simple because it was inspired by the 6502, and ARM is also going to be a useful platform to know in the future.
http://www.bbcbasic.co.uk/bbcsdl/index.html
Also not a bad choice is the Atari ST. The 68000 series CPUs are really friendly to program in, and again you get a nice simple flat frame buffer. FaST ST BASIC is BBC BASIC for the ST, with built in assembler.