It depends on what you want to know. CIL is an assembly language for a theoretical machine (or virtual machine) called the CLR , which is implemented in software. The CIL code is then compiled by the on-time compiler into an x86 assembly or a 64-bit assembly.
If you are mainly programming in Visual Studio, I would recommend that you first study CIL for the following reasons:
1) CIL is much simpler. The x86 build has evolved since the 1970s, and it really shows. The number of instructions is huge, and you will need to study irrelevant technical details to get started.
2) It will be easier to write well-structured programs. If you later decide to explore the x86 build, I hope you take these habits with you.
3) CIL will be more useful if you ever want to configure your .NET programs at a low level, as this is what they are compiled to. This is the last place you need to optimize.
Reasons to study x86 / x64:
1) This is assembly language for real equipment. This means that what you learn will be "real." You will also learn a lot about how the actual equipment works. This does not mean that at first it would not be easy to learn a simpler language.
2) There are registers on the platform that you cannot recognize using CIL.
3) The platform does not have built-in object-oriented functions, which means that you will need to learn how to implement them yourself. This is something you can also learn about through C ++.
In general, I would recommend learning a simple language like CIL, JVM assembly, or LC-3 assembly, as Daniel Wolfe suggested. If you also want to learn about x86 builds, you can always do this after that. Learning how to in the correct order is probably easier than just learning the x86 assembly yourself.