Sure, there are “common Linux commands”, but I doubt that you'll find statistics as to which ones are used most often on average, and different people use different commands. There is no authority who will say “this command is common, this one is not”.
There are commands that are standard across Unix-like operating systems, defined by POSIX. However standard is not the same as common. Some commands get standard by the virtue of having existed for a long time and having been included by many vendors. Commands such as
tsort are standard, but you may well never use them —
compress has been superseded by better compression utilities such as
tsort is a fairly obscure functionality. On the other hands, commands such as
mount are de facto standard, but not de jure, because the way they operate varies too much. And there are commands like
bash itself for which only one implementation exists and that are very common.
Non-embedded Linux systems, as well as Cygwin, come with GNU coreutils. This is the package that provides basic commands like
mkdir, etc. (and
tsort). The util-linux package is also pretty much universal across non-embedded Linux systems. BusyBox is a set of utilities that covers the same ground as GNU coreutils and util-linux, but with reduced functionality, for embedded systems.
There is no definitive list of common commands, but there are many books and tutorials about the Linux command line. I suggest that you read a few of them, little by little. And of course, when you need to do something, go and look for the command(s) that can accomplish this task. In addition to web search engines, you might find the apropos command useful — for example, if you want to copy a file, you can run
apropos -s 1 copy and it displays a list of commands whose short description includes the word “copy”. As
apropos both includes a lot of false positives (“copy ID3 tags”, “system-to-system copy”, …) and can miss commands because their description used a different formulation, you'll often have better results with a web search engine which attempts to rank results by relevance and popularity.
I will offer a short list of useful commands. This is by no means an exhaustive list, nor even a list of the commands you'll use the most often, but they are common tasks and it's very useful to know them.
grep — search in text files
less — view the content of a text file
locate — find a file based on its name, when you don't know in which directory it is
ls — list files in the current directory
man — view the documentation of a command
xdg-open — open a document, like clicking in a file manager