Simple accessible microcontroller for learning low level digital logic
If you want to work directly on the hardware without using other peoples code libraries then assembly language is probably a good option.  Each assembly instruction will translate directly into an executable word of machine code.

Coding machine language directly is usually very tedious and not done my most people.

The choice of a microcontroller involves many factors.

1)  How complex is the CPU core and instruction set

If you are just starting out you probably don't want to pick an ARM, x86, Power-PC, or MIPS type microcontroller.  The instruction sets are usually quite complicated.

The Atmel AVR series of microcontrollers is easy to learn.  Specifically the AT-Tiny and AT-Mega types.  They have 16 or 32 8-bit registers.  They understand 50-ish instructions.  They support multiple interrupt vectors.
http://www.atmel.com/products/microcontrollers/avr/

The PIC16 and PIC18 series of 8-bit microcontrollers are very simple.  They have only one working register.  Some of the PIC16s have as few as 30 instructions.  The PIC type microcontrollers access memory using a bank select register field, which adds some complexity when writing programs.  They support one high priority and one low priority interrupt vector.  Some of the PIC-16 MCUs are so stripped down that they don't have built in debugger support.  Use of the debugger makes it much easier to write programs so keep that in mind.  The PIC-18 MCUs do have debuggers support on every chip I have used so far.

http://www.microchip.com/design-centers/8-bit

8051 based CPUs are simple, made by many different vendors, and have been around for decades.  The 8051 CPU is often embedded inside of other chips when a vendor wants to add programmability.

2)  The software development tools.  You don't want to pick something with tools that cost a fortune.

The tools for the AVR series microcontrollers is called Atmel Studio, and it is free.

http://www.atmel.com/tools/atmelstudio.aspx?tab=overview

Microchip corporation offers MPLAB-X for free for developing with PIC series MCUs.

http://www.microchip.com/mplab/mplab-x-ide

3)  The available development kits.

The JTAG ICE3 programmer from Atmel costs around $53 and programs most of their AVR microcontrollers.

http://www.atmel.com/tools/jtagice3.aspx

Microchip corporation offers development kits such as the curiosity development board (with integrated programmer) for as little as $32.

http://www.microchip.com/DevelopmentTools/ProductDetails.aspx?PartNO=DM164136

The general purpose Microchip programmer MPLAB-ICD3 costs around $199.

http://www.microchip.com/DevelopmentTools/Listing.aspx?CatID=bc05135f-75a9-4aa6-a6c5-82bdc9903a4c&amp;LeftNavId=bc05135f-75a9-4aa6-a6c5-82bdc9903a4c

4)  The user community.  Both the Atmel and Microchip microcontrollers have good user forums.

http://www.avrfreaks.net/

http://www.microchip.com/forums/