I'm trying to learn about how compilers, operating systems, and computer systems work internally. Here's my current plan:
Any tips or recommendations would be nice. Thank you in advance!
My first advice is to read a high level book on the subject. That is, I am assuming you haven't done this yet, and were planning on simply working along with some online tutorials or something. At least for me, I tend to want to dive head first into things like this, but then I quickly feel in over my head and then just give up the project. Making sure I have a really good high level understanding of projects before starting helps me tremendously.
One series I might recommend are the Write Great Code books. I can't vouch for the whole series as I haven't read them all, but my office has them at work and I have used them a number of times to get a pretty good grasp on the subject before I dove headfirst into something. For instance, and one example that may relate directly to your plan, I was needing to understand how the GCC compiler organized the ELF binary it generates, what each section is, and what is stored there. (This was for an embedded system and we were expanding our RAM so I had to reorganize some stuff...)
You said "Nothing too hard"... In my opinion, I think your steps are already pretty difficult, especially if your end goal is to learn about compilers and operating systems. I would skip this whole virtual machine, at least for now. In reality, processors are pretty simple, and based on the fact that that you already know that it just processes a 'machine language' you probably already have a good starting grasp.
I would instead start with step 3 and just writing your own compiler. I took a compilers class in college and by the end of the semester, I had a working Pascal compiler that I built from the ground up using LEX and YACC. It was quite enlightening. You might also look at Bison as its used in conjunction with yacc for such things. I've never used it though.
Also, simply doing little exercises in your free time, like figuring out how to manipulate GCC to compile hello world into less than X number of bytes will teach you a lot more than you think about how that stuff works. (There are quite a few examples of this on the web, by the way)
Have Fun!