I'd say that before you begin you might want to take a look at the Dragon Book and/or Programming Language Pragmatics. That will ground you in the theory of programming languages. The books cover compilation, and interpretation, and will enable you to build all the tools that would be needed to make a basic programming language.
I don't know how much assembly language you know, but unless you're rather comfortable with some dialect of assembly language programming I'd advise you against trying to write a compiler that compiles down to assembly code, as it's quite a bit of a challenge. You mentioned earlier that you're familiar wtih both C and C++, so perhaps you can write a compiler that compiles down to C or C++ and then use gcc/g++ or any other C/C++ compiler to convert the code to a native executable. This is what the Vala programming language does (it converts Vala syntax to C code that uses the GObject library).
As for what you can use to write the compiler, you have a lot of options. You could write it by hand in C or C++, or in order to simplify development you could use a higher level language so that you can focus on the writing of the compiler more than the memory allocations and the such that are needed for working with strings in C.
You could simply generate the grammars and have Flex and Bison generate the parser and lexical analyser. This is really useful as it allows you to do iterative development to quickly work on getting a working compiler.
Another option you have is to use ANTLR to generate your parser, the advantage to this is that you get lots of target languages that ANTLR can compile to. I've never used this but I've heard a lot about it.
Furthermore if you'd like a better grounding on the models that are used so frequently in programming language compiler/scanner/parser construction you should get a book on the Models of Computation. I'd recommend Introduction to the Theory of Computation.
You also seem to show an interest in gaining an understanding of operating systems. This I would say is something that is separate from Programming Language Design, and should be pursued separately. The book Principles of Modern Operating Systems is a pretty good starting place for learning about that. You could start with small projects like creating a shell, or writing a programme that emulates the ls command, and then go into more low level things, depending on how through you are with the system calls in C.
I hope that helps you.
EDIT: I've learnt a lot since I write this answer. I was taking the online course on programming languages that Brown University was offering when I saw this answer featured there. The professor very rightly points out that this answer talks a lot about parsers but is light on just about everything else. I'd really suggest going through the course videos and exercises if you'd like to get a better idea on how to create a programming language.
