I would recommend a microcontroller approach, msp430, avr, or one of the many arms. You can get an msp430 or one of the arm launchpads from ti for about 10-20 bucks, you can find stm32 based discovery boards for 10-20 bucks as well, the stm32f0 (cortex-m0) is simple, basic. The stm32f4 is loaded with stuff like caches and an fpu, but still a microcontroller.
I think the microcontroller approach will take you back to the roots, very basic stuff, the hardware doesnt have video usually or hard drives or anything, but you do learn how to master the tools (compiler, linker, etc) and how to read the manuals, etc.
You could just fast forward to linux capable hardware like the raspberry pi or beaglebone. At all levels but in particular the linux capable levels, in addition to the manuals for the video chips, usb chips, etc you also will want to use the linux source code to learn from. Understand that the linux drivers are often very generic and often contain code to drive a whole family or whole history of hardware from one vendor, so a bunch of the code may not match anything in the manual, but some will and that is where you will get over the hump of understanding what the manual is saying. Doesnt mean you have to re-write linux in order to use this information.
Start small take it one step at a time, pcie and video alone from scratch is a major task, if you start there you are quite likely to fail unless you already have the knowledge and experience (if you did you wouldnt be here asking).
An approach you can also take is bochs or something that emulates an old 8086 DOS system, and if you can find some good, old, dos/8086 based manuals you can poke at regisiters, cga mode, vga mode, etc. The disc controllers can be difficult still, etc...
There are plenty of arm, avr, msp430, mips, etc (and x86 but I wouldnt go there for this until later) instruction set simulators that would avoid the cost of hardware and also avoid the cost of damaging the hardware and having to buy more (it happens even with lots of experience), even better writing your own instruction set simulator...vba some nds simulators, working your way up to qemu.